The Mileage Plus miles you get from Emirates trips are redeemable miles only -- they don't count as elite qualifying miles.

The general rule is that trips within the Star Alliance network (CO, US) earn EQM and RDM, but "Mileage Plus Airline Partners" (Emirates, TAM) earn only RDM. Sounds like you've already found the charts at http://www.united.com/page/article/0,6722,1177,00.html.

To hit Premier Executive on UA, you'll need to earn 50,000 EQM within the calendar year. If you're already invested in the UA program, getting the extra RDM may help you with awards, but these trips won't help you improve your status.

You're right that you'd earn more Emirates miles than UA miles for your business-class travel -- you earn 125% UA miles for business class trips or 150% Emirates miles for business trips. The math works out if you figure AKL-DOH is about 9000 miles each way.