Any creature that meets the prerequisites for the feat Dragon Steed (Draconomicon 105) can take the feat, and those prerequisites—Charisma at least 13, at least 8 ranks in the skill Ride, and the ability to speak the language Draconic—aren't even that difficult to meet. A dragonnel (151–2) even has an Alignment entry of always neutral: typical dragonnel mounts don't even usually have any conflicts with your everyday blackguard.
However, the creature's description says that a level 9 or higher paladin can have a dragonnel instead of another special mount anyway—no Dragon Steed feat needed—, and there are some things to keep in mind if you're not replacing a special mount with a dragon steed.
First, according to the dragonnel's description, instead of taking the feat, any creature could've purchased for about 10,000 gp the services of a dragonnel. Generally, folks avoid taking feats they can buy, but, nonetheless, a multitude of reasons may make actually taking the feat more attractive.
Second, exactly how much like a cohort this dragonnel is remains up to the DM. That is, an actual cohort gains XP (therefore eventually advancing in Hit Dice or class levels as is the DM's whim) alongside the creature the cohort serves. Whether or not this occurs with this dragonnel—that's "much like a cohort" yet gained 5 levels earlier than it would have been as an actual cohort via the feat Leadership (PH 97)—is the DM's call. While a level 5 dude gaining a CR 4 critter as a buddy is pretty awesome, that same level 17 dude might regret his choice if the DM rules the critter doesn't advance alongside him.
Finally, while a dismissed or slain cohort acquired via the feat Leadership can typically be replaced in 1d4 months (DMG 105), whether or not a dragonnel acquired via the feat Dragon Steed can be replaced in a similar fashion is also up to the DM, again hinging on how much like a cohort the creature actually is. If the DM rules not that you've befriended a pack of dragonnels that lets you periodically fly off on their young and instead rules that you've befriended Brysass the Strong, Defender of Strovamri Pass, then replacing Brysass could be problematic if not impossible.
In short, if playing a long-term campaign, before taking the feat Dragon Steed and not using the feat to replace your special mount, ask the DM how "much like a cohort" the dragon steed is. If the answer is Not much, instead of taking the feat, save up the cash and just buy a dragonnel if you want one.