Hi there, welcome to the forum!
A couple things:
You should get her spayed. Her litter box habbits will likely stay bad until you do, and female rabbits have an 75-80% rate of uterine cancer if unspayed. it is important to find a rabbit-savvy vet to do this.
Dribble urine makes me think it could be a urinary tract infection, or her marking because she is unspayed. I think a vet visit is likely in order.
Does she use a litter box in the cage, or is the whole cage her box?
second, clumping kitty litter is very dangerous for bunnies if they ingest it. I (along with many other ppl on this forum), use compressed pine pellet litter (sold cheaply as wood stove pellets or horse stall bedding, more expensive as “feline pine”). For first litter training, carefresh is great, because many rabbits like to toilet on soft things.
Also, I know you didn’t ask for this advice, but that is a very small cage… you can easily give her more space 24/7 by adding an x-pen “front yard” attached to the front of her cage, and then keeping her cage door open. Check out the “housing” section on this forum for more ideas on how you could improve her home. Often rabbits have poor litter habits when in small cages, because they just think of everything as the toilet.
Finally, a few weeks is a short time for her to trust you. Here are some tried and true tips for bonding with your bun and earning her trust:
– First, and very importantly, be sure that your bun can come out of it’s cage/hutch/pen/condo on it’s own. The pen/condo/hutch should be your bun’s “safe space”. If your bun’s home is elevated, you can use a ramp or steps to allow it to come and go as it pleases.
-Only pick her up unless absolutely necessary. Never do this just to spend time with her. (and please research the correct way to handle a rabbit to make sure you don’t injur her)
– Once your bun decides to come out to explore, play “hard to get”. ignore her. Lay on the ground while she is out, read a book, etc. If she comes up to you, don’t try to pet her (yet). Be patient and calm around your bunny. Respect if they want to be left alone. “floor time” is seriously one of the best things you can do.
– Hand feeding! You should feed at least some of her veggies and pellets by hand. You could do this with just the first few leaves of veggies of the day, or a few pellets when you give them. Fragrant herbs (cilantro, basil, mint, fennel) are all good at enticing shy buns. Talk to her calmly when you feed her so she associates your voice with good things.
– When she has become comfortable enough with you that she will lay down or relax near you on the ground, you can “ask” her if you can pet her, by placing your hand on the ground in front of her, so your pinky is on the ground and the back of your hand is facing him. If she puts his head down, she wants you to pet her head! If she doesn’t, then don’t force it. Stick to petting only the head and ears until she gets really relaxed with you. The back and bum are very personal and sensitive areas for rabbits.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.