Yes Nick/Leverick Bay will take care of you.

Normally they have cars in the parking lot at Leverick. I believe the front desk holds on to the keys. You then take the car and drive to the car rental company to fill out the paper work and you are on your way. Very simple in fact.

Just make sure when you head off for your island adventure, you take the National Parks permit or you will have to pay to enter The Baths!