Does a female rabbit build its own nest?

You do not need to build the nest.

The doe will bud the nest herself, using straw and other materials, and fur from her belly.

You should thus provide extra straw for her to build with.

She will keep them warm this way, don't touch the kits!

The doe will only be with them a few times every day, but she has not abandoned them. Just don't touch them.