IF you are departing/arriving into class G you still will need to make the appropriate calls regardless of the rules of your flight, and if you are concerned about a conflict you should make a call on the local frequency. On the odd occasion where I am not on a local frequency, its usually heading onto class C or D so I have centre on one com and tower/approach on the other com. In this case, I ALWAYS make a call on the CTAF/local broadcasting my current position and altitude stating that I am changing to the approach frequency.
On the centre frequency, The controllers know where you are, so no real need to give a call. You will hear it all the time from Centre, ie "unidentified VFR traffic n miles to the SE at 6500, intentions unknown", and the other aircraft will usually respond with "copy traffic" or something similar.
However, if you want to let centre know, just call them up and say "Brisbane Centre, tecnam 1234 is currently at dunwich 1500 tracking direct to jacobs well" . I personally would not bother unless conditions were marginal.
There is one massive bonus you get from monitoring centre frequency, is that they will often broadcast potential conflicts.
There is a bit of conjecture about what frequency you should monitor (ie local or centre), and casa just published some guidelines on this. I cant find them at the moment but I will try track it down the next couple of days. My personal opinion is that if you only have one com, monitor ctaf below 5000, and centre above 5000. I wouldn't make that a hard rule, but its basically outlines where my attention is focussed when flying with 2 coms.