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Unless you are BM specced, just bring the lowbie pet with you in any instances you hit. It should get quite alot of xp just by standing next to you.
If you should choose this rout, I would suggest asking your group about it before hand. If they are expecting you to bring a level appropriate pet to help the group through the instance they may not react to your low level pet very well.
In addition to instances you can farm low level greens for profession supplies or items to sell on the auction house. You will end up meleeing everything, unless you prefer to practice kiting. If you can group with even one other person to keep agro it makes the pet leveling much easier.
I tamed a spider that was 30 levels below me and leveled her up. It was a lot of work, but it was worth it for me. However, I’d prefer to never do it again. *smiles*