Congrats!
Most propcollectors will tell you - as will I - not to sign 99.9% of the props. They should stay as they are. Get a great photo of her to go with the piece and have the photo signed. If you ever need to sell the prop the signature on a prop will hurt both the value and how many people would want it. As a propcollector myself I don't touch signed pieces (with very few exceptions).