What great fun! If I was a cat, I'd want to sleep in there for sure (when it's open, of course). What did you attach the fabric and fur with? Did you remove all the hardware and then reattach it? The outside looks like it came that way and was treated really, really well.
HA! I just scrolled down to have another look before posting this and saw a cat in the mirror! Apparently a cat does want to sleep in there!