
Most ordinary health insurance policies do not cover animals used for breeding purposes for breeding related issues, such as infections passed from dog to bitch & bitch to dog.
You would need to contact the insurance companies to find one that might cover breeding dogs & bitches.
I don't know what else you would need to insure for a dog being used at stud. I don't think you would get cover for things like your dog becoming sterile, failing to get a bitch in whelp, changes in temperament etc