I picked up my puppy at MCO and flew back to LAX with her in first class on United. In fact, that's why I returned via UA versus Virgin America as VX wouldn't let me travel first class with her (understandably as they don't have the below seat storage). She's a Maltese and all of 2.2 lbs, so her carrier fit under the seat.
However, were I to do it again, I'd travel VX-- I find that I liked VX coach better than UA first.