BRU-LHR-SIN has only two legs. Not sure what the reference to third leg is, but if you are catching a connection at SIN on to Australia on QF, then as MoreMilesPlease notes, in practice your bag will be interlined and you will just pay the one fee at BRU.

This is also the official rule per IATA Resolution 302. Although QF does not honour this resolution, as you won't be checking your bag with them they won't ask.