Webster's Dictionary has it as woman or prostitute with no derivation. Partidge's Dictionary of Slang and unconventional English has it as woman, especially one readily available, traces it from US to Canada c1925(!) and suggests it comes from "broad beamed", noting that in Australia "broad" could mean "bottom".
I had thought it might have derived from Broadway and the denizens thereof, so once again: Truth :1 Roger :0
RtS