If OZ are not prepared to through check onto VA and especially if you are on a non-Australian passport the queue times for passport screening and customs can be very unpredictable during this period. While a connection on separate tickets is doable, there is quite a chance of queues and a risk of misconnect.
Oh, poop. I am both expecting OZ to not check my bags through AND am traveling on a non-Australian passport. I'm really hoping three hours is sufficient. Would I be needing to connect to a different terminal? Is there lots of walking involved here? Thankfully, we'll be arriving as J pax and also departing (on VA) as J pax.
Also-have you ensured that you have the appropriate visa for Australia? You may have a onward ticket but you may still require a visa, especially if you wish to self connect on separate tickets.
As a US citizen, I've already applied and paid for our e-visas.