Presuming you have a reasonable tool kit with your trailer then it should cover any needs you have with the generator. The only extra items we carry if we plan on taking our generator is a gas container and dining fly. The dining fly serves double duty as a generator shelter if the weather turns wet.
I should point out that our generator needs never include running the air-conditioner - basically just recharging the battery and periodically running my wife's hair dryer and also the vacuum cleaner. With just these needs we can go close to a week without having to refuel our little Yamaha 1000.
Jay