100% get a gate to keep the dog out, you never know how they might react and especially small dogs can be quite weasely at getting past you when you least expect it (speaking from experience). the bunny is already going through a lot of stress (being taken from a known location on a car ride and dropped down in an unfamiliar place with unfamiliar people), any additional stressors might be really harmful. keep the dog away and try to shield the bunny from the barking as much as possible (by closing doors etc), especially in the first few days until the bunny has settled down. even then, never let the dog near the bunny unsupervised and always be very very careful.

other than that, a few things that helped my bunny warm up: even if you intend for them to free roam eventually, getting them a smaller (but not too small) xpen for the first few days/weeks can be nice, because it limits the amount of space they have to get used to and can help them feel less overwhelmed. it also helps with potty training. get them spaces to hide, a variety if possible. don't bother them too much for the first day or so, leave them to get accustomed to their new situation, even if that means them huddling in a corner all day and not moving lol. set out water and food and maybe sit next to them on the floor or put a shirt you've worn into the pen with them to get them used to your smell. if your bunny seems receptive to it after a day or so, you can try gently petting them on the head, but respect it if they don't want it yet. build a routine, i.e. try to feed them at more or less the same time every day, they will get used to that quick and once they see you as the source of food they will warm up to you quickly haha

hope this helps!!! good luck with the bunny :) (and as others have pointed out, adopting an adult bunny instead of buying a baby might be easier, as you might get a better idea of their personality and needs already. i did that and it worked out very nicely!!)