Now now Wiz.....
Having a degree as opposed to no degree means that you could be better positioned when competing for similar positions in an airline. A degree of any type is almost a must in the USA, however as Wiz rightly pointed out Australia is unique.
At the end of the day it comes down to supply and demand. For me, I have no degree, however nearly all of the cadets I fly with have degrees ranging from Mechanical Engineering to Computer Science. For them, they were able to gain their current positions and no doubt had an advantage compared to other candidates who did not have such an education level or qualification.
These days some of my colleagues are even pursuing a 'Bachelor of Aviation'...and good luck to them!!
So supply and demand is the key, perhaps contact the airlines you want to work for and see what they say.
Good luck!!
b.