If you're new to puppet making I wouldn't recommend making a replica as a first attempt but you can carve it out of a block of foam, cut it down the middle so you have two halves, hollow out the space for your hand, then glue the two sides back together. Covering it can be done by flocking, but that's more of a professional option. You can try covering it with antron fleece, or any material that similarly hides seams, but it may be tricky with all those curves of hers.