keep your miles
if I were you, here's what I would do: keep collecting miles on Continental since you already have over 11k miles with them and you don't travel much. Get a continental credit card which will give you one airline mile per dollar spent each month. Put all of your bills, books, food, gas - EVERYTHING on that card and pay that one bill per month. Just watch your money carefully! Watch for special promotions where you can earn double miles, etc
Continental is partners with Qantas so I would not think you'd have an issue getting to Australia at all.
best of luck!