Car seats can be rented at most car rental agencies in Aruba. However, I would make sure that you reserve your car rental before you go down/make sure the company that you are renting for has car seats to rent to you with your car rental. There are a number of links to car rental agencies in this website that would rent car seats with a rental.

As for the stroller, I would bring your own stroller (perhaps just an umbrella stroller). When you get to the plane to board, they will take your stroller and load it on the plane for you. When you get off the plane, your stroller will be waiting for you at the exit (it is not inconvenient to bring it with you and it does not count against the weight of your luggage that you are allowed to bring on the plane). You certainly want to have a stroller in Aruba as it is safe to walk around Aruba and it is very helpful have a stroller at the beach, at a restaurant etc. (provides shade/your baby can sleep in it etc.) Furthermore, your child would probably be more comfortable in his/her own stroller.