Might as well have it from the man himself as well. From the notes to Now I'm Easy in The Eric Bogle Songbook Volume 2 CD:

"A 'cocky' is an Australian term for a farmer who farms land on a small scale and is therefore usually poor and battling to make ends meet. It is derived from the contemptuous term given to to these farmers of "Cockatoo Farmers' by the large rich graziers".

Jon