Practicing in Perth

I don't really know where this should go so I'm putting it here.

First, a bit of backstory. I'm doing a four year masters in maths from Bath, and I'm currently in the middle of my third year, which I'm doing abroad, at Penn State. However, once I graduate my plan is to spend a year practicing seven shades of excrement out of the saxophone (eight hours a day plus, I already try and do at least two on top of my degree) because I'm already damn good at it and would much rather make a career out of music than maths. Unfortunately I didn't realise this till some way into my maths degree, but, you know. I've alloted myself one year to see if I can get good enough to make it, after which I'll give up and get a real job if I don't cut the mustard, which hopefully the maths degree will make fairly easy if it ever comes to that.

However, the reason for the post is that, as an englishman, how easy would it be for me to do this in Perth, Australia? Obviously I'd have to work part time to support myself (I do not require or expect a high standard of living for this year) but already I was making fairly decent money with a regular jazz band back home before I left and I reckon I'd make a pretty good teacher, be it music teacher or maybe maths tutor.

I wouldn't normally be looking to do this in Perth but since being in America I've met a girl from there and we would quite like it not to have to end once we have to return to opposite sides of the world.

Am I being stupid? Could this ever work? Would the australian government ever grant me a visa to, as far as they're concerned, essentially bum around for a year?

Thanks.