Skye - congrats on taking the step to come to Sydney - I'm sure you'll have a ball!
Does the university offer any assistance with finding accommodation? I know that when I was working for Sydney Uni, I was involved in helping to sort out some apartments, shares, or flat-sits for visiting staff in medicine faculty.
Considering you have a child, I think you'd welcome more room than a studio. Consider also Five Dock and Ashfield, suburbs the same distance out as Drummoyne, but in a direct line to Uni. Not quite as salubrious as Drummoyne, but quite nice, plenty of parks, amenities - I live quite near there.
I'll put an email address in my profile for a short period, if you want to contact me direct with some questions - I'm not always lurking here. Do you play tennis?