Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.601 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)

"It does not mean you can have a free stay in Sydney unfortunately since SYD-MEL on UA would be cabotage (in most cases, a foreign-flagged carrier cannot fly passengers on domestic itineraries)."

Maybe yes, maybe no. The fact that you cannot book SYD-MEL as a free-standing flight on UA does not necessarily mean that you cannot book SFO-SYD (stopover) - MEL as a single ticket on UA. Depending on Australian restrictions UA might or might not be permitted to carry post-stopover passengers from SYD to MEL.