The difficulty bonus is just from fighting higher level mobs, I thought? Don't think you get anything for fighting things you're weak to.
If you don't even have a 25 yet then what you're really asking is "how do I level my first pet to 25". Fight stuff in the wild, do the questline and fight trainers for bonus exp and the loot bags, etc etc.
Look, just go destroy things with the FFF. Insert cat, receive exp.
just take him around one day to all the trainers for the dailies, even the non bag ones. That should get the job done. If you just wanna grind mobs go to the fields around that farming and cooking place in MoP and use a level 25 flayer youngling. Most mobs are critters and he just destroys them. Also theres a stable like 10 feet away.