Thanks very much the responses everyone - much appreciated!! The second LAX would be a transit only.

However, I tried to book this today and hit a snag. Two travel agents in Sydney said that I am not allowed to do the Australia domestic flights. Apparently, they are only permitted if connecting to an intercontinental flight. EG you could do DRW-SYD-SFO etc...., but not what I first proposed. This does not seem to be reflected on the online rules. Interesting! Any thoughts!