Unless you can visit with the antidote to his allergy, I would be wary about staying at a large resort, where many of the meals are buffets. I think you would be better off at a small hotel, where you can easier customize your meals.
If a meal is individually cooked for your husband in a restaurant, it is possible for you to actually go into the restaurant and actually check what goes into what he will be eating.
While peanut oil is not standard, it is used. I would stick to small hotels and restaurants where you can see for yourself the ingredients used to prepare the meal.
If you decide to stay at a resort hotel, choose one that has restaurants where individual meals are prepared and stick to these.
Regarding medical care, towards the end of the DR1 health page, we list the medical center most hotels in the Punta Cana area refer their patients to. Note that most Punta Cana hotels have physicians on their staff.