It looks like a fun trip you've got planned.

I can see a couple of issues, however.

First, you're backtracking. From Europe/Middle East you head to South-West Pacific, then backtrack to Asia. You must travel in a continuous direction, either eastward or westward. (Note, however, you can backtrack within regions (for example, you could fly PER-SYD-MEL-BNE).) So in your itinerary, you would need to go something like DOH-CMB-HKG-KUL-AKL-MEL-LAX (or DOH-KUL-CMB-HKG-AKL which, at a guess, would probably give you more miles).

The Americas are also a problem for you as again you are backtracking. You travel to LAX, then to South America then back to North America. You'll need to visit one of the Americas and then the other. One option would be to change AKL-MEL to AKL-SYD then fly onto South America from there on either LAN or Qantas. With this option I would aim to have your last North American stop as JFK because JFK-LHR is obviously a longer flight.

Do you want to finish in CAI? You only need to finish in the same region (Europe/Middle East) and the LHR-CAI flight is operated by a 767 so I'd be aiming for something a bit further afield and with a better aircraft (eg. DXB).

That's a few preliminary thoughts but others with more knowledge than I will jump in.