Dollies generally do NOT have a breakaway - they have no battery to engage an electric brake. A dolly with surge breaks might have a mechanical breakaway.
State dolly and car towing laws are full of loopholes; the usual trailer-tow laws rarely apply. Dollies themselves are mostly exempt from the trailering requirements, and a dolly + a car is considered a vehicle in tow rather than a trailer. Plus there are gray areas of interpretation. For example, rear lights are typically required when a vehicle is towed, but most law enforcement considers the vehicle's own lights to fulfill that requirement. However, if the vehicle doesn't have working rear lights, the dolly needs to provide them. For that reason, new dollies usually come with lights.
This is also a case where the common practice very likely deviates from the letter of the law. Most RVers put the car of the dolly and go. The smarter ones have brakes and stop/turn/tail on the dolly. Safety chains but probably no breakaway.
To be 100% sure, you would need to research the individual state along your route. Good luck with that!
