For more control over the timing of the relocation, you can definitely apply for a new service, then email email@example.com
to move all your history / email accounts / etc to the new servcie, then cancel the old. This guarantees that you have no downtime.
It's even easier than that Corey, on the relocation form:
Date You Request to Cancel Current Service:
Start Proceedings of New ADSL Service:
If you are moving and already have a new phone number, start the proceedings 'right away', and specify the cancellation of the current service to be whenever you last expect to use that, the date you cancel can be after the start of the new service.
Telstra don't have relocation options, so we send a cancel request on 'date you request to cancel' and we send a new order on 'start proceedings of new adsl service'. The customer data is migrated as part of that relocation.
This gets complicated if you want to keep the same number, what happens there is when the number is moved to the new address, the systems can take 24 hours to update, the order is put in, the phone service at the current address is dropped (because the number is moved), so that causes the internet to be lost.
The new order goes in and gets activated, downtime is a necessity to keep the same number.