Are you worried about legalities or a successful trip?
The legalities vary from state to state. Some states require brakes on any trailer over 1500 lbs. UNLADEN weight (trailer only, no cargo). Some states require brakes on any trailer over 3000 lbs GROSS weight (trailer plus cargo). Then there is Alaska, which throws 5000 lbs. GVW into the mix. Perhaps just to be different.
Some states have a "Braking Performance Standard", such as Montana does, in that you must be able to stop any "combination of vehicles" within 40 feet from 20 MPH on a clean, level, dry, hard surface. Montana also requires brakes on any TRAILER that has a GVW of 3000 lbs. or more.
IMO, you will probably be OK with a trailer gross weight of less than 2000 lbs without brakes. However, if it gives you ANY concerns, for your own peace of mind, get the brakes. You don't need the additional worry.
Electric or surge brakes will work just fine.