I have sold in auctions for many years. I buy my staging items to put around my subject, and use them over and over. This is what I would do:
Solid colored items for girls (not white), use "material" that is a baby girl pattern as cute as you can get. For boys solid colors, use a baby boy pattern material.
White items for girls look awesome on a draping pink background, light to royal blue for boys, also with the draping look.
Items that have a busy pattern for girls, you can use white lace in a draping effect for the background. Boys you can use plain white material in a draping effect for the background. It looks fantastic too, to use one solid colored material with another solid color material that match your item and overlap them and drape them in the background.
When your baby girl is in it, it would be cute to sprinkle tiny silk roses around that match the hats, then of course take it away before they try and eat them. lol ... you can use tiny stuffed toys that compliment the hat to for staging.