I use a sunscrean for sensitive skin instead of baby sunscreen and have never had a problem with it. The thing is, even the baby sunscreens haven't actually been tested - it's illegal to test things on babies! The cancer council recommends keep babies covered up instead of putting on sunblock. Not helpful when you're going out for a swim, but just thought you might like to know.

I think just try different sunscreens and use the one that she doesn't react to (if there is one).

P.S
I'm in perth too, and IT IS REVOLTING! Thank goodness we have an airconditioner. Trouble is, its only in my parents bedroom so the four of us have been camping in there all day lol.