Well, being fast still has a lot of value, even without a specific move that takes advantage of it. But there's also a lot to be said for the P/P breed of [pet]Spectral Raven[/pet] ... or even the 301-speed P/S.
I looked up your collection, and you're still at the stage where widening your roster in general will be of more use than focusing in on specific niches, so I don't want to encourage you too far into a corner with birds and bird-like species. I laid out the stages of progress in battling here, and you are on Stage 2: https://eu.battle.net/forums/en/wow/topic/17623632232#post-3 so my advice would be to focus on the pets that will best get you through what you need to achieve to master the content, and only then loop back to pick up your personal treats. Do please read that whole post. The list of pets there, and the addons, is what will get you through the achievements ... and unlock pets like [pet]Chi-Chi, Hatchling of Chi-Ji[/pet].
However, there certainly are some bird treats along the way.
[pet]Ikky[/pet] is a really good pet for PvE. I completed all BfA world quests excpt Rogue Azerite with a team of [pet]Ikky[/pet], [pet]Zandalari Anklerender[/pet], and [pet]Iron Starlette[/pet].[*] Ikky is a glass cannon that will take down most things with Black Claw->Flock->Savage Talon (if the opponent is even alive after Flock).
Any turkey - [pet]Turkey[/pet], [pet]Highlands Turkey[/pet], [pet]Plump Turkey[/pet] - has Food Coma, which stuns the opponent, and because you're a flier, it will probably go first while you have the racial. This is a niche trick, but has some useful applications. In PvE, it forces a tamer to swap pets. Or you can use in in a wild battle to stun the opponent, swap in a levelling pet, and swap it out again without taking damage.
The S/S [pet]Robo-Chick[/pet] is quite fun. Its Wind-Up delivers quite a punch, and Overtune gives it that instant speed-up, which can make other breeds viable for speed. Its Batter hits an extra time if faster, though, so that keeps the S/S breed as my favourite.
[pet]Junglebeak[/pet] and [pet]Axebeak Hatchling[/pet] has the same abilities, but the [pet]Mechanical Axebeak[/pet] you have is a different case, but also one of my favourites. Using the Flying speed racial, it can drop that Decoy first, and then attack from behind it, or use it to protect a levelling pet. It can unleash that Haywire from the safety behind the Decoy, and Beast attacks do weak damage against it, so it's an ideal Beast double-counter.
Rain Dance "Heals you for [about 300] and increases your team's hit and critical strike chance by 50% for 2 rounds" so in the context of using it with Nocturnal Strike, you swap it in, it takes a hit for the swap, it heals with Rain Dance, and then Nocturnal Strike, which normally has a 50% hit chance, gets an extra 50% hit chance from Rain Dance, so it will always hit (except for some dodge mechanic on the part of the opponent).
With the Blighthawk's Cyclone, the Rain Dance increases the number of hits the enemy team will take from Cyclone, and the number of crits done by them.
[*] I explain that team here: https://eu.battle.net/forums/en/wow/topic/17623172161#post-9