If you're using clumping cat litter, dump it out immediately. If a rabbit eats it, it can actually kill them. If it's regular cat litter, they are too dusty for bunnies. The only cat litters that are rabbit safe are Feline pine pellets (non clumping kind), and Yesterday's News pellets. Some other good ones are other brands of pine pellets for animals (if you get the wood burning stove ones then you have to make sure there aren't any accelerants added to them), aspen shavings, Carefresh bedding, shreaded paper, Kaytee granule small animal bedding, you can even use hay. You may be able to find some of these at Walmart in their small animal section or the feline pine and yesterdays news in the cat section, or also at petstores, or you can also order them online. Just remember no other kitty litters except the two I mentioned above, and absolutely no clumping litter. You'll also see cedar shavings and pine shavings advertised for rabbits, but you shouldn't use them. They both have oils in them that are bad for rabbits. A lot of people on here like the pine pellets cause you can buy a big bag for pretty cheap if you get the kind for horse bedding or the wood stove pellets. The Carefresh can be kind of expensive. If you use shredded paper you just want to make sure she's not eating it or you'll have to use a different kind of litter.
She's still a baby so it might take her a while to get really good at using a litter box. Is she peeing in there? It might be harder for her to use the litter box right now because of her hurt leg. You'll probably just have to clean up alot until her leg gets better. As long as she's peeing in her litter box she's doing good. Rabbits just usually leave their poop everywhere, but she may get better at it. If you get her spayed when she's older, then that sometimes helps.
I'm really glad she seems happier today
She's probably just getting used to being in a new place. That can sometimes take a little while. The grass cave sounds good. It's a good chew toy for her too.
A few things about rabbits that are important are being really careful about giving sugary things because in some rabbits it can get them sick. Learn what good rabbit poop looks like because if your rabbit ever has tummy problems, you'll be able to tell first by their poop changing. There are two kinds of good rabbit poop, the normal round ones and their cecotropes. If it's soft, runny, too big and too small, or irregular shaped, or if a rabbit stops pooping and eating, then it means there's something wrong with their tummy. So when you clean Taz's cage, it's always good to just look at her poop and make sure it looks normal and that will mean she's not having any tummy problems.
Here's a good website that will tell you stuff about having a house rabbit.
http://www.rabbit.org/
What kind of hay are you feeding her and are you just buying small bags of it or do you get big horse hay bales?
