You just want to make sure you are feeding more than an adult portion of pellets, as babies need more. An adult portion for that type of rabbit would be about 1/4-1/2 cup so a baby would need almost double that, but this amount would only be if there is no mushy poop or digestive upset. If there is then the amount may need to be reduced a little. And also make sure to feed unlimited hay. One other possible reason for the soft poop could be that you are feeding broccoli and carrots. 9 1/2 weeks is a little early to be introducing veggies to a baby bunny if it isn't something they were fed when they were with their mom. It's usually best to wait until they are at least 12 weeks old, so that their digestive system is more developed and can better handle the new foods. Carrots and broccoli aren't the best veggies to start with either. Broccoli is a cruciferous veggie and can sometimes cause gas and digestive upset for some rabbits. Carrots are high in sugar and can cause mushy poop and bacterial imbalance if fed too much of. They are considered a treat and should only be given in very small amounts, and only if there is no mushy poop or smaller than usual poop. Better veggies to start with when a bunny is old enough, are leafy greens like dark leafy lettuce(never iceburg), parsley, cilantro, carrot greens. And like any new food(except usually grass hay), they should be started in small amounts and increased gradually, looking for signs of digestive upset.
This link has some good info on introducing veggies and diet info for rabbits, though their info on non cruciferous veggies isn't correct, as some rabbits can get gas from them. So always introduce those very cautiously if at all.
http://rabbit.org/suggested-vegetables-and-fruits-for-a-rabbit-diet/
I have buns that like to sleep in their litter boxes too, and them getting dirty from it is never an issue. If you are using wood shavings, that might be your problem. Try using wood pellet litter. It's cleaner and less likely to get caught up in the fur. I also put a layer of hay over the wood pellets. This makes it softer for my buns feet, as the pellets are a bit rough and they don't like that. Then each day I sprinkle a fresh layer of hay over the peed on hay. This also helps keep them cleaner.
Using wipes is a good alternative to bathing, and bathing should be avoided except in very rare instances. If a rabbit is getting soiled and dirty enough that it requires a bath, and doesn't have medical issues causing this, then something needs to be corrected in the rabbits life/environment to ensure the rabbit is staying clean.