You have to do some of your EMS placements + rotations blocks with small animals, which will involve a lot of closely handling dogs. At vets, most will be stressed too, so even normally friendly ones are going to be louder and have a higher potential to thrash or bite etc so really you need a certain degree of confidence for this. While you could probably ask them to be put away, a lot of horse yards and farms will also have dogs there, and if they aren’t getting in the way etc it would probably not make the best impression to do so. So all in all, my opinion as a vet student is no you wouldn’t be able to avoid dogs. As others have mentioned, have you tried getting help for this? Therapy is the best way to go if you really want to be a vet, but if that isn’t available to you for whatever reason, could you maybe ask a friend with a calm friendly dog to maybe try help you get used to being around dogs?