Not sure what a power booster is. You are supplying 120 AC to the trailer through he cord. Unless you have a known low voltage condition either from the Power Company, if so get them to fix it, or because of undersized wire leading to the outlet there is no reason for any type of transformer.
There is nothing in the trailer that would warrant surge protection. While plugged in at home the only thing on the AC system would be the converter. It is a regulated supply so the output voltage to the batteries is protected.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles