The feat Draconic Breath doesn't meet the metabreath feats' type requirements
The feat Draconic Breath (Races of the Dragon 102) doesn't grant a breath weapon "whose time between breaths is expressed in rounds" (Draconomicon 66). The feat Draconic Breath's breath weapon can't be affected by metabreath feats.
The feat Draconic Breath grants a supernatural ability; feats that apply to supernatural abilities can be used with it...
Thus a character could pick the feats Empower Supernatural Ability (Tome of Magic 74), Enlarge Supernatural Ability (Tome of Magic 73), and Widen Supernatural Ability (Tome of Magic 75) and apply their effects to the feat Draconic Breath's breath weapon. (The feat Extend Supernatural Ability (Tome of Magic 73-4) won't do anything.) No further metamagical supernatural ability feats were officially published.
...And so can breath channeling feats
Breath channeling feats (Races of the Dragon 101) don't have the restrictions that metabreath feats have, requiring only a breath weapon. Use those with the feat Draconic Breath's breath weapon; I recommend the feat Entangling Exhalation (Races of the Dragon 101).
Their calculated CR remains the same, but they are far stronger
Carcer rightly points out the way your CR is calculated, but I feel like that doesn't capture the entire picture.
I feel like this pseudodragon may very well be punching above its 1/4 weight with a 2d6 breath weapon. With a lucky roll, there's a good chance it could knock out an entire first level party in a single breath weapon. CR 1/4 indicates it should be roughly 2-3 pseudodragons to form a decent challenge for a first level party, but 2-3 pseudodragons with this breath weapon will absolutely annihilate any first level party round one if they know how to aim.
Ogres suffer from a similar problem. If you calculate their CR, it comes down to a CR 1 creature, but they are still listed as a CR 2 creature, simply because there's a really good chance that it'll oneshot a first level character.
On top of that, you've replaced their attack which requires getting in melee range with a breath attack they can use from a distance. This, combined with a fly speed of 60, means they can very easily fly into range, breath weapon, fly away, and then fly away until their breath weapon has recovered, before coming again for a new run.
This is at a level where most characters will have very few ways of dealing with a flying opponent.
I for one would not want to face even one of these creatures at level 1.
If the breath weapon is changed to be once per short rest instead of Recharge 6, it'll at least make it a lot more manageable because it can't hit and run. Also reducing the damage to 1d6 may very well be enough to keep it around roughly the same challenge rating. It'll at least no longer be something I'd really dread fighting at level 1.
As an aside, regarding being used as a familiar (say, for a Warlock via Pact of the Chain), it's most likely not that big a deal, I doubt it'll be more impressive than invisible scouts. Familiars used for combat purposes tend to be dead familiars before long. It'll be good for killing some goblins every now and then, but it'll be costly to keep resummoning your dead familiar.
Best Answer
Dragons do need to breathe (note that black dragons have the ability water breathing, indicating that a dragon without it can't breathe under water and is subject to drowning rules), so anything that asphyxiates them will kill them, regardless of the element. A dragon's resistance to damage of certain elements doesn't save them from needing to breathe, just from being directly injured by that element.
How long a dragon can hold its breath would just use the normal drowning rules, so how long depends on a dragon's Constitution score. (But there's nothing to stop a DM from house-ruling that dragon physiology works differently in their game's setting, so caveat slayer.)