You are correct. I do believe they have 35 slots, although up to very recently they were only allowed to fly 28. With the liberalised air services agreement between the UK and Australia recently signed they could in theory have another flight per day to use up all the available slots. I suspect however that this slot is leased out to someone else (and at a guess it is BA although I am sure someone else could confirm) as if you don't use the slots, you loose them.

QF don't have any spare aircraft at the moment so I suspect that is going to be a limiting factor. LHR requires too many aircraft to operate the route and at present that's going to be a hard issue to try and overcome even with the A332s QF have signed up for. I'm going to bet though that PER or BNE end up getting a direct service should QF decide to use those slots. MEL and SYD just don't make sense especially now that BA have cut capacity to both cities and the JSA between BA and QF mean all revenue and costs are shared.