WoWDB

I don't think you get as much XP carrying pets against these 2 as you do against like Pandaria or Draenor tamers, but you get a few thousand pretty easy, so why not.

First of all, it has to be fairly high level.  Like 15-18+, preferably not aquatic (due to Cyclone), flying (Arcane winds), or undead (Scratch).  Also a CD tracker like Derangement's Pet Battle Cooldowns is really nice here to track Hungry Rat's Arcane Dash.  Without that addon, you'll have to be manually counting rounds to keep track of when it's back up. Now on to the strat.  

Start with P/P breed Emerald Proto-Whelp (2,2,x) against the Hungry Owl.  Put up Emerald Presence.  Then just Emerald Bite him down.

In comes Hungry Rat.  Get off what Emerald Bites you can.  When EPW dies, Swap in your carry, he'll take a Scratch, then bring in Anubisath Idol (1,1,1).

If Arcane Dash is off CD (not likely, but possible), Deflection.  Otherwise, Sandstorm.  Use Sandstorm on CD, Deflection to deflect Arcane Dash, and otherwise Crush.  Keep in mind this team isn't so OP it can overcome a string of bad RNG...and with Sandstorm's accuracy debuff, that's always a possibility.  But it's pretty solid.