Check the articles section on this site as there are some good ones about Australia.

Your brother or one of his co-workers should be able to check flight loads.

I just completed a LAX-SYD nonrev trip on QF with no problems, during busy Mardi Gras season. I'm guessing it would be less busy in April as it's getting cooler there now.

Also, as a UA relative traveling on UA, you'll have low priority but probably not the lowest, as among standbys you'd probably have higher priority than "other airlines (non-UA)" non-rev travelers.