I have a question. I have decided to start working on my very first pet team and I wonder if I might need to change it up at all to be able to level quickly. I am using:
While dragons are very good, especially as "starter" pets, I would suggest getting 3rd pet for your team that's from a different family, to give you more range in moves. As you will encounter many beasts and critters out in the world, I would suggest a mechanical (strong against beast) or a beast (strong against critter). Other choices would be flying (strong against aquatic) or magic (strong against flying).
A few "newbie friendly" suggestions for each type:
Mech - darkmoon zeppelin, darkmoon tonk
Beast - some sort of spider, zandalari baby raptors
Flying - moth
Magic - lantern
For leveling purposes, of your two dragons I'd personally keep the crimson whelp, as the heals are useful for a member of a leveling team.
Go to Karazan, outside there is eyeballs, they fight solo, catch those then go to dragonblight and catch some of the birds on the bones, then go to pandaria and get a waterstrider, now you have multiple level 20s, grats.