Yes, the absence of QFlink availability from ba.com is odd. The oddity used to be more prominent when QF's NZ subsidiary Jetconnect was also listed as an operator of many/most of the trans-Tasman QF-coded flights. Jetconnect availability also did not appear on ba.com but was easily bookable by phone. However, QF has recently changed its operating arrangements so that (at least when I last looked) QF trans-Tasmans are now fully bookable on ba.com.

Off the top of my head, the main advantage of booking multiple flights on one booking (assuming that none of the flights are intended to be connections) would be that if you have to cancel or change the whole itinerary, it is possible that the cancellation or change fees could be less if you're only dealing with one booking as that is effectively capped at £35 for the entire itinerary.

However, if you're looking only at QF domestics, the TFC figures per sector are relatively low and so you'd have to have a lot of sectors in the itinerary for this to have a realistic chance of being a benefit. If you book each sector separately, the cash cost of any cancellation is capped at the TFC figure already paid for that sector, which you'd forfeit on a cancellation. If you want to change the sector, you'd simply book the new flight and cancel the old one.

The downside is that if you book many sectors in one booking, and you want to change any one sector within it, you may have to either pay £35 to change it, or you may have to cancel the entire booking and start again, because of the restrictive re-routing rules on award tickets.

So I normally book my QF domestics separately.