Is that the entire photograph? (Or did you crop it from a larger photo?) if so, could we see the entire photo please? You might find that others might request to see the edges and the back of the photo as there may also be dating clues there.
My first thought was 1950s, but with so little to go on I am not confident about that guesstimate.
Keep in mind that if your grandmother emigrated to Australia, she could have been sent photographs of more distant relatives, even children of her friends etc. Apart from curiosity, is there any other reason you want to identify the child?
It might be useful to put the photograph in context. For example, was this photograph among many others or do you suspect it was special in some way? For example we had a request some time ago where someone had found a photograph seemingly hidden behind another in a frame, which obviously aroused suspicion.
I think it highly unlikely that someone will be able to identify the child based on that image alone. Maybe some detective work might find her though. Starting close to home, do you know all of your great grandmother, and grandmother's children? Might this one have died young? Or been illegitimate?
I think the first thing would be to get an accurate date range for when the photo was taken. Are there any other photos within the collection which may have been taken on the same day, people wearing the same clothes for example, child included in another photo with identifiable people?