Hi, I am bumping this up so that it doesn't get buried. Lots of people here are very savvy about rental cars, more so than I am.
I don't have any special tips on rentals for this island, as I only rent them when I go off island, and I almost always use Priceline. Not sure about Priceline from Australia. This Hawaii rental car broker often gets praise for its prices:
Start with their quote and then go direct to the sites of the major agencies like Alamo, Budget, National, Hertz, Avis, Dollar, Thrifty, Enterprise.
In general, there is no fixed going rate but rather whatever you can find. Most people shot all the sites and make a reservation that is not prepaid and can be canceled without penalty. Many or most continue to shop periodically, and often will find the prices have improved. Sometimes they go up though. So you definitely want to be holding an acceptable reservation.
I think an intermediate size car is good, as you have only the baby in back. They get much better gas mileage than full sized, and a compact is pretty small and hasn't got much trunk space. But it's up to you and what deals you find. Sometimes if you rent a compact, they won't have any when you arrive and they just upsize you for free. You can't assume that though, so you have to rent one large enough to be acceptable to you.
Our parking spaces are all striped for compact--intermediate, so it can be a bit of a squeeze parking a larger car although in fact there are more trucks and SUV's than sedans if you look at what residents drive.
A small or crossover SUV is a nice car for the island, but it doesn't have a trunk and the rental costs tend to be significantly higher if you go SUV, Jeep, or convertible -- unless there's a promotion.
Be sure not to leave the reservation untended to, as you're coming in high season. Oh, and be sure to figure out what to do about the car seat. If you have one you want to bring (and it is good for US specs), you can check it for free, or you will have to rent one from the agency. Some people have complained the rental ones were not nice. Not sure if that is a common issue.