DirectAnywhere
In this case, a CAT3 ILS in Adelaide is unlikely to have made any difference. If the cloud/vis is below the alternate criteria (typically 400'/1600m for airports with low vis. installations) and they had the fuel, the crew would have been obliged to divert. So, it's highly probable they would have ended up in Mildura anyway.
Ah actually no.....
If you are carrying the alternate you try the approach first - subject to reported vis/ RVR being above your company and type minimas. If you don't get in (zero base and either 75 or 100m for Boeing/ Airbus min RVR cat IIIb) then you divert to said alternate.