Personally, I'd be hiring a car or van. I'm not a fan of public transport with kids on holidays - too easy to get stuck or stranded for longer than anticipated and be waiting in the rain etc. Plus if something happens and you need to get to a GP or the hospital or something, taxis are expensive, especially seeing the Gold Coast is so sprawled out, and waiting with a sick or injured kid at a bus stop is not going to be fun (obviously fingers crossed that nothing like that happens, but you have to prepare for everything). Aussienic's right - all the theme parks etc hire out prams etc.

Are you doing the theme parks and attractions while you're here? Can give you advice on deals and good places to go if you like