Ask an aussie where they're from and they will answer - emphatically - Australia first and foremost. Only reluctantly, if pushed, will they mention any nationality of ancestors.
My family came here by choice, on a boat (we still have the boat tickets from the 1800's) and I am an 8th generation Australian.. so I've never thought of myself by anything but Australian. No one really needs to push me to mention British ancestry because I thought that was something that was just generally known about Australia ( ) I am not opposed to the monarchy because let's be honest, it's all just a formality now really isnt it? we could become a republic tomorrow and very little would change here in terms of the country running.