I almost used some Carefresh (we also have a rabbit) but opted for hay (again bought for the rabbit). I don't think the Carefresh would hurt, it's biodegradable and safe for rabbit's to eat).
I remember asking about carefresh here a long time ago - gosh, has it been that long since I was new to BYC?
Some people said it was what they used and it was fine. I ended up using a plastic wading pool for a brooder and carefresh was too expensive to fill that up with, so I went with pine instead.
I work at Petco and in the small animal dept. It's safe for all your critters, except maybe snakes.
When I first had Tom and Jerry, when chicks were still dinosaurs, I used carefresh, shredded paper and just a touch of cedar chips in their outside rabbit hutch/chicken coop.
Carefresh is pretty pricey... We considered it for our brooder but ended up buying Aspen shavings instead (it's a little cheaper and supposedly non-aromatic)