You can also fly on BA flight numbers on something like MEL-SYD-SIN or BNE-SYD-SIN and get your BA sectors that way.
Unfortunately I think getting to Singapore this way is going to be more expensive than using QF or other airlines.
And why would you want to go to SIN that way anyway? It is also typically less flexible (QF and others have many more flights) and less comfortable in most cabin classes (all the more so when QF retrofits the new J seat on the A380).
I join others in saying that the earn/burn rate is quite a complex 'competition' between the two programmes. I can see how some patterns would find BA better, but I can actually see how some other patterns would find QF much better on their long haul redemptions. What I agree with is that the homework has to be done individually, especially as it is worth bearing in mind that a BA silver would not get status bonus on most airlines that they might wish to fly from Australia. Another thing to note is that if you stick with BA you won't get anything on Jetstar flights whilst QF members will get points and some advantages access for (ubiquitous) Jetstar flights on a number of fares. On the whole, I would say that most people truly based in Australia (rather than mixing multiple locations) will typically be better off switching to QF.
Velocity is incidentally a straightforward programme that might suit many.