Don't know of any free ones, but Annerley midwives run a mum and baby group which costs $150, and includes weighing and measuring.
Matilda Hospital runs an excellent group on Thursdays from 10am which costs $60.
All the mums and babies head off to lunch on the peak after Matilda, which is great fun.
Matilda isn't running during August, but will start again in Sept.
Both groups you can just drop in.