This should be usually doable. Assuming the MEL-PER flight is an A330 there's a limited set of gates that handle the aircraft, which are at the end of both piers (ie: gates 11/12 and 23/24 iirc) so your longest walk potentially might be from gate 10 to say gate 23 but just as easily your SYD-MEL could arrive just a few gates down from the departure. Either way I reckon the longest walk would be, for most folks, 10 minutes. It is tight, but doable. Of course there's always the chance the inbound for PER could be delayed and it's a non issue.
If it was me though honestly I'd see if space was available on an earlier flight out of SYD just to be sure. You're looking at a peak departure slot out of SYD of 1730 and there can be delays. Now if one is lucky and you get a sweet runway config at SYD you can have a very quick light (last week we were in the air 5min after push back which was very very quick and we arrived in MEL 25min or so ahead of schedule). However all you need is a long taxi and a 10 minute delay in departure and you could be in a bit of trouble. Later in the day any issues that crop up can cause cascading delays (potentially) that can affect ops (weather, etc). I'd be less worried, for example, if it was 7:30am than 7:30pm for that factor.
While QF absolutely SHOULD hold the PER connection since they absolutely know you're on the way, it doesn't always happen. I wouldn't just assume it to be a given, and as noted above connecting checked bags are a separate issue that may or may not get there in time.
In theory you shouldn't need to worry about it. it does meet MCT and MEL T1 domestic is pretty easy to navigate and move around. I guess comes down to the comfort factor of having that time buffer.
I realise you're talking reward seats so this could be tricky trying to get an earlier flight out of SYD with availability but it's worth asking the question imo. Just for peace of mind.