I couldn't find anything on the Quicken (Australia) website about which version of QuickBooks was necessary to be able to use it via Windows Terminal Services so, after waiting 10 minutes on-hold to ask a simple question, here's what I found out.
QuickBooks Premier and above can be installed on Windows Terminal Services.
If ugprading from another QuickBooks version (e.g. Plus), then you get 5 x user licenses (current upgrade price is around AUD$845.00).
If buying new, only 3 of the licenses are enabled and the cost is about AUD$1,449.00
Hope this helps out someone else in the future.