Oh I hear you. My daughter would say the same thing! I do agree that first you need to clarify that she means a toy and not a real dog! :) I also think looking through toy catalogs is a good idea.
My first thought was one of those push button ones that sings and dances Christmas songs or some other catchy tune. You can find them at tons of places! Wal Mart, Walgreens, Target, Calendar Club (these usually open in the malls near the holidays and are pretty cool stores actually), etc.
Also, maybe she'd be interested in a Fur Real dog. They don't dance, but they do walk and bark and my daughter really likes hers.
Good luck, I know the stress of finding "The Present"!