Hey there. Your bunny and dog are adorable, btw! I'm in a place I can type easier now
When bringing your new bunny back to your house, remember that moving from one home to another is quite stressful on a rabbit. She's just getting adjusted to her current place and now she will be brought to another place. You'll need to give her some time to make that adjustment.
When you bring her home to your room, I'd suggest keeping the dog out of your room for awhile. Give bunny some time to get used to the new place. She should actually be kept in the confines of her cage for 48 hours minimum. This is especially important if you want her to eventually free roam in your room. She needs to establish the cage as her space alone and that is the easiest and quickest way to do that. It also gives her time to own her litterbox and know where it is.
When she's first allowed out to roam in your room, it should be just part of the room. Use an x-pen or similar to wrap around her "current cage. By offering her space in small increments, it helps her to feel less intimidated and ensures she has no doubt as to where that litterbox is if needed. The last thing you want is for her to have a potty accident from having too much space. That is a difficult habit to undo.
As for introducing her to your dog, this is best done while she is in her cage. I have a step-by-step process I've used that is explained in more detail (and with photos)
here. As I mentioned earlier, it is important that the dog gets to see your rabbit in the place that bunny will be. You will be teaching your dog that your new rabbit is another member of the "family pack" and that the dog is
not going to be alpha over the rabbit. Of course there are no guarantees. It will depend not just on your training but also the genetic disposition of your dog towards rabbits and the rabbit herself. Pet rabbits, though, are usually tolerant of dogs. There are a few that are very afraid of dogs, but that doesn't seem to be the norm.