Well all teams will always have their pros and cons.
your biggest con are birds I think - especially 1 raven or crow you can probably just forfeit :p
But try to think of other popular battlers, and think if you can win of them.
Say enemy valkyr: if you start with valkyr too, it's dangerous to use the haunt or you risk losing your valkyr.
But you can soak with crawdad, it won't take too much damage. So let's say the enemy valkyr is dealt with if you make it dot crawdad.
anubis: dangerous pet. if your valkyr didn't face him initally. During sandstorm your haunt will only tick for about 70dmg on another pet. And anubis' demolish will probably crush your bunny and crawdad. (Rabbit can keep it busy, but it won't have the damage to take it down properly). But in the end valkyr should win over anubis. So anubis is okay, but dangerous if your valkyr isn't dealing with it.
(All pets with demolish should be banned from the tournament because it's broken
enemy crawdad: I'm not sure your pets can kill another crawdad. your valkyr is weak in damage. Your rabbit is probably super fast and low on damage + no dots...
healing teams in general are painful for your team (sunflower, ruby droplet,...): it will mainly depend on your valkyr, since that is the main source of damage. But valkyr is easily dealt with for them too. Sunflower easily outheals all the damage a valkyr can do. ruby droplet can skillfuly block the curse of doom.
raven/Crow: you're dead, you can't heal. Faster than rabbit. Strong vs crawdad.
moths: tough, I would say you lose if valkyr didn't damage it to get it below 50% asap (so rabbit can deal with it)
direhorns: If they have the shield ability, making haunt very weak I think you likely lose. Your rabbit will get 2-3shot and they outdamage crawdad's healing.
imp: not much trouble: weak dot on the rabbit. Easily outhealed/shielded by crawdad, valkyr is strong.
mechanicals with mines: highly annoying because you must swap in and out quite often with this team.
bone spider / crawling claw: curse of doom: since valkyr is probably "dead" it either ends up on your rabbit (which you can dodge when it's 2 rounds remaining, no issue) or on your crawdad, which is weak. Death grip isn't really an issue.
flayer youngling / scalded basilisk / vermling / hopper: Since your rabbit is faster than any of these I don't see a problem.
if crawdad takes the shield ability this is also little issue for him.
Ragnaros: rabbit can handle it.
animus: with some good guessing and dodging/burrowing the heal, it should be no issue for rabbit.
aoe teams: since your valkyr is dead most of the time - so taking no damage - it should be okay
dot teams (a simple bleed / poison / burning) : Quite painful or annoying at least because you'll be swapping pets often, so 1 enemy pet can dot multiple of yours.
potential con: you can't change the weather.
so now it's up to you to either think of a strategy against teams where I think you should lose. Or just gamble and accept you have a high chance of losing from those. In the end you will ALWAYS have weaknesses of course.
Personally I don't really like the crawdad playstyle. All the swapping involved, and slow killing. Your valkyr deals most of its damage while dead. Your rabbit is a master of dodging and burrowing. Do you really need that crawdad for heals ....
But that's personal preference
I'd replace crawdad with death adder or some anti-healing pet.
imo jademist is too predictable, thus dodged / blocked /avoided, and weak.