blow.n.gasket:
The destination must have 1 or more Cat 11/111 ILS
With WX equal or better than CAT11/111 minima.
Alternate for destination must have one or more CAT11/111 ILS approaches
With WX forecast to be equal to or greater than CAT1 RVR.
If the forecast/actual weather at Perth requires Cat II/III, then it's likely the same will apply at Pearce. I'm not familiar with QF Reduced Alternate Weather Criteria, but if what you say is correct then it sounds similar to the standard ICAO rules. If the destination requires Cat II/III, then the alternate must be equal to or better than Cat I. If Pearce has the same weather as Perth (ie Cat II/III), then it won't be suitable as an alternate.