Checked through baggage when flying QF/BA

I have Melb-Sydney flight with QF prior to BA flight Sydney to Singapore/London, all booked on one ticket. Given all booked on one ticket, I'm assuming bags in Melb will be checked through to London and all boarding passes will be given in Melb. Can anyone confirm?

Yes - you will have your bags checked all the way through and receive your boarding passes for all flights on the same ticket at checkin.

Yes, you will have no problem