It would be good start if they conduct BPL when their premium players not playing any important series. Why would anyone watch BBL (except locals) when their own players playing in the high profile series at the same time (For ex : Australia VS India)
Normally that's what they do. The BBL is usually conducted during the December-January window, when normally the Australian team does not play any bilateral series. This year, however this may change. Limited time period may be available and there may be an overlap between the matches of the national team and the BBL season this year.
you know that one of the biggest events of the ICC is T20 world cup, but till now it is uncertain whether the world cup will be held this year due to coronavirus pandemic. so, I don't think BBL could be held during this epidemic. If BBL will held exclusively, then it is almost sure that BBL will never be held during the national team, because it will lose their business and no 'Domestic League' will want to take responsibility for a loss project.