You should be OK, especially with the 37c tires, but a lot depends on your riding style and skills. Some people are very careless and don't know to lift their butts out of the seat to go over a bump, ride through curbs, and just generally have bad riding technique. This actually matters more than weight. Butted spokes and a deep strong rim will help a lot.

That said, you are sort of on the cusp of where thinking about more spokes would be a good idea. 20-30 years ago, I'd have probably told you yeah, go to 40s, 48 in the back if you ride like a gorilla. Nowadays, I'd say try it, pack light, and ride carefully. Camping gear is lighter than it used to be.