First, animal companions normally grow with a ranger; as you level up, your animal companion automatically improves. That’s normal. It’s also normal that when you get a more powerful animal as an animal companion, you count as a lower level with respect to the benefits the animal gains for being an animal companion. (This is not, however, the same as the animal’s “level,” which is a term that refers to something quite different and is probably only confusing in this context—the level we would be interested in is your effective druid level, because the animal gains bonuses based on that.)
Second, panthers are (bizarrely) not explicitly on the official list of animal companions (nor are mountain lions, cougars, pumas, or catamounts, to cover the myriad names for that species). In fact, so far as I can tell, these animals don’t exist anywhere in the official rules—your links are to unofficial, homebrew creations. You’d have to clear them with your DM to begin with, and even when you do, that homebrew doesn’t include any rules for when they would become available to a druid or a ranger. The panther you link, however, is much stronger than what a ranger has available at 6th level, and the dire panther is much stronger than what a ranger has available at 10th level.
With the books you have available, the first cats you officially see are the cheetah and leopard at effective druid level 4th (which means ranger 8th); both of those cats are somewhat smaller than a panther (and much weaker than the panther you linked). At druid level 8th (ranger 16th), lions and tigers become available—both a fair bit bigger than a panther (and stronger than the panther you linked, but weaker than the dire panther). Sandstorm adds a serval available right from druid 1st (which means ranger 4th).
So, officially, you could start with a serval1 at 4th, and upgrade to a cheetah or leopard at 8th, and then, if you wanted, to a lion or tiger at 16th. Or just upgrade the cheetah or leopard per the animal companion rules. And you could call all of these a panther at various stages of maturity, the same creature using different stats as it ages—the same as with dragons, though at a much faster timescale. A reasonable DM should have no problem with that description of your animal companion’s stats.
The real problem here, however, is that you’ll notice that these levels are all much, much higher than the druid levels: ranger animal companions are really weak. The halved effective level means that your animal companion will basically never be safe in combat. The halved animal progression means it is good for a scout, and that’s it. To get an animal companion that is actually good, you kind of have to be a druid.
Which is really, really dumb. Druids are massively, overwhelmingly powerful spellcasters, one of the top 5 in the game without question. For them to also get the best pet is absurd. And the ranger is a really inconsistent, unfocused class—you can use it to pretty good effect if you mine all the books and magazines for select features and turn yourself into something of a powerhouse, but using just the core books (and Complete Arcane), you cannot do that. As such, of the two classes that have an animal companion, the weaker one for some reason also gets the weaker animal companion.
I would recommend talking to your DM about switching druids and rangers with respect to animal companion progression (that is, rangers getting the full-leveled one, druids getting the half-level one). With that progression, the panther and dire panther (on a really really quick skim, I am not vouching for the work) seem more reasonable options at 6th and 10th. With the halved progression, though, they’re probably twice those, 12th and 20th.
- Or a housecat, if you really cannot use the serval. Note that housecats are not listed as an option for animal companion—because they are too weak. As such, your DM probably won’t mind you using one. He might even allow you to use the urban companion rules rules, which do allow the housecat as an option (with some benefits to offset that) temporarily until you get your cheetah or leopard—though it would be kind of weird if your pet suddenly got dumber.