It should be no problem at all, with your mother escorted all the way and installed on the flight to Brisbane. But why not give BA a call and check on the precise arrangements? I presume your mother is booked with them as a passenger needing special assistance.
But is there any reason to go through SYD? It's a long, long trip from LHR, even in Club World, and even for the fit and hardy. So if your mother is frail it would be much better to fly LHR-BKK-BNE or LHR-SIN-BNE on BA/QF, and avoid the transfer in SYD.
In any case, I wish you mother a safe and comfortable trip. If she does go through SYD, I'm sure it will be fine.