I would recommend doing a pre camping trip in your driveway before heading out. Hook up water and power and give all your appliances a go. Your fridge
btw will need a number of hours to cool down to use anyways. I usually plug the trailer in and cool down the fridge
the day before heading out.
At a minimum you should take along:
A few levelling blocks
A basic tool kit - that includes a roll of electrical
and duct tape.
An assortment of fuses that your trailer uses.
A couple of hose clamps of various sizes
A tire iron - the one for your tug may not fit the trailer.
First Aid kit
Extra batteries for your flash lights
A voltage meter.
Spare pre greased wheel bearing and a seal... never know where/when you will have a failure and it could happen in a location where the ones you need are not available.
A credit card!
There are a few old threads that will give you an good idea as to what all people carry with them.
Stocking Your First Trailer
Putting together a Tool Kit
What do you always keep in your egg?