A Toyota Yaris for the week will run about $200. If you price the cab ride to and from the airport and a few trips around the island(especially if you go to Flying Fishbone or Old Man and the Sea to eat on the beach with your feet in the water), you will find a car to be more cost effective.
For the 3 year old, I would definitely recommend the Baby Beach. It's about a 40 minute ride from the SC, but a great place for a toddler to swim, look for fish, etc. I also heard last year of a petting zoo that opened near the little church on the northern side of the island which might be a good place to go. That might be the Philips Animal park the previous poster mentioned. The butterfly farm is small, but there are a number of unique butterflies inside the closed area that you can walk among. If you go early in the week, I think you can go back in later in the week as many times as you want without paying another admission.
As for places to eat, check out the Aruba bb for recommendations, as there are many good places to eat. Can't really think of any restaurants good for a child, except maybe the Buccaneer which has giant fish tanks, but so-so food.