We are travelling from London to Perth, by British Airways to Singapore and Qantas to Perth. Tickets have separate PNR's (Qantas tickets thru FF points). Can we book our baggage thru to Perth or should we re-checkin in Singapore?
As BA and Qantas have an interlining agreement, this is entirely up to the good will of the BA check in desk at London, as your travel is in two separate legs with separate tickets.
There is no way to guarantee any other answer.