I also recently flew with my baby. The attendents didnt even knew I had a dog with me!!
I put her under the seat (in a soft sided carrier) and midway through the flight was able to take her out and let everyone coo over her
I was told that she had to be put back in for landing for her safety but as long as I held her on a leash she was allowed to sit with me. I flew on Express Jet (not even sure if they are a company anymore) but it only cost me $50 to fly her and less then $200 for me. It was great