First of all, thank you to those who replied.

I would definitely consider the spring or fall months due to the weather details given. I am sure I'd rather spend some winter time in Australia compared to Michigan.

My preferred carrier is Delta as I am getting a few miles on them. I do not know if they partner with another airline or codeshare for the LAX to SYD portion but some details in searches show they do one or other.

Hope that helps....