We just have the coles baby parks and it says "Baby parking" or something on the sign.
There are only 2 parks, so they're often taken up. We use them for our shopping and we don't take the pram shopping ever, we carry DS2 to the trolley while holding hands with DS1. I only use that parking basically until they grow up and can hold hands and don't need to sit in the trolley seat, baby capsule or other seat.
I don't park there if I've got not kidlets with me though, and I do check out the cars in those parks to see if they have a baby/kid seats in their car. LOL. I'm so nosey.
I think you have the right to park there whether or not you use the pram too.
xx

