Just wondering... dogs and camp nursing?

Many camps will allow this; you'll just have to ask around. I don't know anything about shih tzus, but do consider how well they'll do in the outdoors (including variable climate) and especially how friendly they are with children. If there's any chance that they could ever snap at kids, they don't belong at camp.

It'll depend on the living quarters, too, because of course they can't be wandering around the health center. But it's worth a shot.

At my camp dogs are not allowed during the camp season. I take my Portuguese Water Dog during the work days but camp insurance policy dictates the rules. Last summer one of our staff sustained a bite on his face that required stitiches. It was the maintenance's director's dog who was in the directors house but on camp property.
The dog had to go. Our camp is only 15 acres and the nurses station right in the middle of the camp. No place for dog to do it's business. I have a therapy trained dog who will only go on command when we are out. So ask questions of the camps you are considering. Make sure your dogs are crate trained. They should not be left in the nurses station loose if you have an emergency to go to. And you might have to crate them when the nurses station is busy and you can't be supervising all the strangers the dogs encounter. My daughter is a groomer and the breed you have is a wonderful dog.