Don't forget to seal the wood well or to line it with some sort of plastic. I would do both. Use a sealant and then use plastic drawer liners with the sticky back to do the entire inside. Otherwise you work will be in the garbage in a few months.

What are the dimensions of the bookshelf? You don't want it to be thinner than 12" minimum, the rats shouldn't have to bend their necks or tail to fit when they turn sideways or they can end up with permanent issues.