get your parents to try the local baby shops - often they either do the hiring or know the people that do and they will hire out a whole range of stuff, prams, cots, seats, highchairs etc. If you are going to be doing this trip a lot it may be cheaper for your folks to buy a cheap $30 kmart/big w stroller if bubs is old enough by then.

malakili is right though the car rental companies hire it with your car (although check it when/if you get the car cause their installation ability often leaves a lot to be desired) - they used to be $5 a day but I think with some they are up to $10.

in qld the ambos hire out the capsules for newborns but i don't know whether they hire out carseats for bigger bubs.