Sorry F3G. I forgot what the original question was - i.e. "Can you book a flight using an Australian passport. "
Yes, you can book a flight regardless of passport you have. However as F3G rightly points out make sure you comply with Ryanair's requirements. If you don't comply you do not fly. Many people get caught out with the requirement of having 6 months left on passport on arrival. Many countries insist on this including EU ones - even applies to fellow EU citizens!
It is also worthwhile knowing that Ryanair on line check in is NOT available to everyone. As F3G states check the T & C's.