It is good that you went to the vet!! That will give her the best chance of survival. The GI bacterial imbalance can cause so much damage so quickly because young bunnies have a very unstable population of bacteria in their gut. If you think about it, they're born with (almost) no bacteria in their gut. They feed off mom for ~6 weeks, and during that time, they only have to digest milk, which is really simple to digest, and they're protected by their mom's immune system. Being with the mom helps them because she passes her GI bacteria on to her. The most important bacteria are in the cecum, that makes cecotropes, which are those poops that they eat. The mom eats her poops, licks herself and her babies clean, and that's how she passes these good GI bacteria on to her kits. Then the bunnies can move on to solid food around 6 weeks of age and slowly test the GI bacterial population they have, until they're adults and have finished growing and have a stable gut. Between weaning and 6mo-1yr of age, these bacterial populations aren't very well established--they've only been there for a little while, and getting the correct balance of bacteria can be difficult. Any stress or diet change can quickly cause overgrowth of some of these bacteria, which can kill the others, so that you only have one species in there. That one species is too much--they grow out of control and release toxins into the body of the rabbit. They can't digest the rest of their food properly. The diarrhea and toxins can very quickly lead to death.
As for how quickly the URI has progressed, again I think it has to do with the immune system. After weaning a baby rabbit no longer has its mom's immune system to protect it, so it has to develop one of its own. Going through something stressful, like moving to a new home, can cause one of the opportunistic bacteria that are always present at small amounts in the rabbit to grow out of control, because stress suppresses the immune system. Because the immune system isn't mature, this type of infection can go out of control.
Juts like human babies, the immune system of a young rabbit is very weak. In particular, their GI bacterial populations aren't well established. That's why diarrhea/mucous in a young rabbit is an emergency in my book, and we've seen too many times that it can be deadly. :cry1: Just like you have to take special precautions around young human babies, you have to be really careful with rabbit babies. Laws require you in many states to not sell baby rabbits before 8 weeks of age. Even after 8 weeks, they need to be treated extra gently to keep them healthy, such as minimizing stress as much as possible.
I'll be praying for you guys. I'm glad you have the medicines you need to have a chance to beat this.