I think a lot of people solo old raids, but way fewer actually play the battle-pet games.
3.6 Million pet battles a day
900k "PvE Instances" (Raids, dungeons and scenarios) a day
Although it may seem more people raid/dungeon/etc by way of mouth, the actual numbers show a vastly different story.
Unless you have a super rare pet, mainly TCG, you won't be making a small fortune, alas it also depends on server, pets can be an excellent way of transferring money to another server.
Only pets I've bought off the AH were Darkmoon Zep & Tonk, the faire wasn't on, and I actually needed them for the celestial tournament, they were already lvl 25, they were around 3-4k each (I also bought them on another server that had them cheaper, this also impacts price and actual sales as they are account wide), and the only reason I bought them is because I needed them, anything else I've bought petwise was because it was ridiculously cheap at like 100g.
Similar to mounts, I see the Crimson Deathcharger listed by the same people week in, week out, never selling, and if you started that quest from scratch, it takes far longer than farming any of the rarest farmable pets.
Breeds can determine whether a pet is extremely usefull or complete garbage. It also depends heavily on if the pet is difficult to obtain, whereas pets that are exclusive to normal/heroic (like the Dark Quivering Blob and the Droplet of Y'shaarj), but also pets that are from bosses that are a bit more difficult or impossible, but nothing really is, to solo.
I have noticed that the actual pet cages are displaying pretty badly or not at all, which can be quite annoying if you have several pets with different breeds.
All in all, it may just be your server, I suggest looking up theunderminejournal.com