carpet? no. A short pile fleece, Minkee, short pile faux fur, or even a really fuzzy brushed woolen fabric would be far better choice. Carpet isn't meant to flex, the inside is very rough, and frankly gluing it to a surface as flexible as legs when walking wouldn't last 50 paces.
You can order swatches from on line fabric retailers, this will give you a better idea than the pictures.
I totally understand not wanting long fur legs for this character, that isn't right at all.
Minkee would be the most comfortable, but as it is geared toward baby products it tends to come in baby colors (I've seen a chocolate brown once, and a very pale grey, but never black or any bright bold color ever. I don't think it's easily dyable, you'd ruin it's finish texture).
Begin your search, the right material is out there, you just have to put in the search time.