Its probably easiest to wait till close of business. In order to do this using Windows Explorer you will need to limit your underlying connection between the 2 systems which is not trivial - generally this is done at the router level (as it is not part of Windows Explorer - unlike, for example some SCP clients which have this functionality built in).
You havn't mentioned the speeds of the points, but if they are both faster then 10 megabit, and if you can find out how to do it (old hardware, playing with the negotiation speeds of one of the network card on your machine), a hack might be to force your NIC to 10 megabit which will limit this.
Stepping back though - I'd imagine the latency between Perth and Sydney is not inconsequential. You may find that, providing you move stuff 1 file at a time, the performance of your network might slow a bit but be quite tolerable due to the "stepping down" of the performance of the transfer due to the distances/latency involved. As ironic as it sounds, even better if there is a bit of packet loss between the sites [For TCP connections - which these are - Packet loss acts as a signal to slow down the transfer ]