I would layer it with quilting batting, make a fabric frame around it, and put the same fabric on the back of the batting. Then do a small quilting "stitch in the ditch" between fabric border and picture. It will be very sturdy.

You could make a little pillow.

Might look cute on the doorknob to her room.....closet door?

I turned cross stitch projects into pillows for my kids when they were little. But I like the fabric-frame/quilt batting idea. I think it would be really cute like that.

I like the pillow or even a bell pull if she has a narrow wall space in her room- my daughter's room had a narrow space between the window and her closet, directly across from her door.