We are about to play a new campaign and I have been itching to play a dragon with the rules from the Draconomicon. We are starting from the bottom at 1st level characters. Is it OK/balanced/allowed to play a dragon as a 1st level PC? My biggest concern is the ECL as the lowest is 5. As a relative new player I'm not quite sure: does this basically mean I'd be equivalent to a normal level 5 character?
It’s a problem but perhaps not as bad as “ECL 5” suggests
You are probably more powerful than a 1st-level character should be. You are not, however, as powerful as a 5th-level character can be, or even should be. Moreover, even as a 1st-level character, Wyrmling White Dragons have some glaring weaknesses that don’t seem appropriate.
The LA system is poorly-designed
What must be understood is that the LA system was apparently written by people who didn’t really like the idea of players choosing “monstrous” races – either from a story perspective or from a “we haven’t really figured out how well that’s gonna play out because we’ve been focusing on the more usual choices” – and as a result Wizards “overpriced” nearly every LA in the game. As a result, whether it was intentional or not, the ECL/LA system effectively discourages players from choosing these races, and punishes those who do despite it.
You can see this, frequently, in the fact that LAs are often higher than CRs on the same creature. There’s something to be said for things sometimes being more potent in players’ hands than they would as an enemy (things at-will certainly can fall in that category), but Wizards overdid it.
The biggest problem is actually skew
The real major problem is that monstrous races get things that “regular” PCs cannot get, while failing to get things that PCs usually cannot avoid.
For instance, an ECL 5 character has a base of +2, minimum, in every save, and at least one save is going to be more like +4. They’re going to have 8 ranks in at least a couple of skills, and that’s going to allow them to take feats and get into prestige classes that require those 8 ranks at level 6. Most importantly, they’re going to have 5 hit dice: between 12+4d12 (avg. 38) and 4+4d4 (avg. 14) base HP, plus 5-20 more from their Constitution score. Level Adjustment gives none of these.
Meanwhile, LA’d races give inordinate amounts of ability score bonuses, and sometimes other features, that PCs usually simply cannot get. In the case of the Wyrmling White Dragon (which I’ll address in detail below), that includes the Flying and Burrow speeds (it also includes the breath weapon, icewalking, and [Cold] subtype, but those are less impressive).
This leads to cases where monstrous characters are “too good” in some things, and “crippled” in other areas. Something with very-high ability scores might have some ridiculously high skill checks, and especially ability checks, but cannot take feats appropriate for their ECL because of having fewer ranks. That same character who is trivializes skill-based interactions is a massive liability in combat because of very-low HP and saving throws, perhaps. And so on.
The result is simply that the system does not work very well.
But the Wyrmling White Dragon is a particularly problematic case
Unlike some of the problematic cases I mention above, the Wyrmling White Dragon has very bad ability scores: +2 Con, −4 Int, −4 Cha.
In exchange, you get to cause some headaches for the DM.
The flight speed is pretty nice, but by level 5 it’s not that special. At level 1, though, you might be untouchable: if I were DMing for you, I’d find that at least mildly annoying. But the Burrow speed is actually a bigger problem, seeing as burrowing is a good way to mess up dungeons – “oh, no, we’ll be skipping all the traps and ambushes and just digging straight to the treasure, thanks.”
Otherwise, the breath weapon is very weak. You don’t get freezing fog or other spell-like abilities of white dragons, you don’t have any draconic spellcasting, and icewalking barely matters much of the time. And the vulnerability to fire arguably hurts more than immunity to cold helps, since fire is the more common damage type.
So basically, you get to fly, and if your DM doesn’t ban it for making it impossible to design dungeons, dig. You can breathe a cone of ice, but pretty soon you’ll be better off not doing that most of the time. Your ability scores, saves, skills, HP, and base attack bonus are going to be permanently penalized rather seriously as a result, and you’re in serious danger of even minor enemies who happen to use fire.
Better solutions for playing a dragon
Number one, there are a ton of dragon-themed classes; I particularly like the Dragonfire Adept from Dragon Magic, if you have that book. Great beginner class, too.
Meanwhile, Races of the Dragon has a number of playable (as in, LA +0, actually pretty good, causes no headaches) draconic races. Dragonborn and spellscales get the Dragon type, which has some nice features, plus the perk of being able to claim that you actually are a dragon. The Dragonwrought feat for kobolds gives them the Dragon type as well.
The argument about whether or not these races count as “True Dragons” is long and tortured; I don’t really recommend getting into it. Just ask your DM if you can claim to be a true dragon for story purposes – his answer should probably be something like “you can call yourself that, good luck getting the bigger dragons to see things your way.”
Combining these, you have the Dragon type, with all the perks that go along with that. You can also take levels in Dragonfire Adept, gaining things like flight, a powerful breath weapon, and some spell-like abilities, much like Dragons do, but in a level-appropriate manner as you grow.
Yes, there are some pretty major problems with this from a balance perspective.
Dragons have supernatural and spell-like powers, unusual defensive and attack features, and racial hit dice. If you're looking for a mechanical prohibition on playing a dragon at level 1 (instead of just comparing all the goodies they get to the features of a typical level 1 PC and going "Naaaah"), racial hit dice is where it's at.
LA + racial HD (+class levels) = effective level.
To determine the effective character level (ECL) of a monster character, add its level adjustment to its racial Hit Dice and character class levels. The monster is considered to have experience points equal to the minimum needed to be a character of its ECL. - Monster Manual 290, or the SRD
The weakest (and thus lowest level) of the True Dragons listed in the core Monster Manual is the white, at (as you've seen) an LA of +2 and 3 racial HD for an ECL of 5. This means the game thinks it's the equivalent of a level 5 PC.
This means you'll probably be tougher, able to deal more damage, and have more utility than anyone else in the party... so much so that the rest of the party will perish in the face of an enemy that poses only a moderate threat to you, or you will be able to handily destroy most enemies that would challenge the rest of the party. On the other hand, against some enemies the opposite will be true. KRyan's answer goes into the mechanics of this in great detail. The takeaway is that balancing encounters for a party like that is going to be nightmarish for your GM.
You'll also have to consider that being a dragon is weird.
Aside from obvious concerns like increased armor costs (Armor for Unusual Creatures, PHB 123), you're a dragon. Loot dropped for the rest of the party may often be useless to you. The GM will have to do a lot of work to make level 1 puzzles and traps (which assume, for example, that the party doesn't have access to flight) challenging. Your presence in cities and towns will be noted and responded to drastically. People will want to hunt you, or ask you for favors.
In short, being a dragon in a normal party will almost certainly make the game about you, both in-game and out, and not about the group.