First, welcome to FT!

A couple of comments...

If you're beginning in August and going first to Miami/Bermuda, you're flying straight into the hurricane belt at the peak season. You don't indicate the amount of time you'll spend in various areas (six months overall, but no subtotals) so it's hard to say if re-arranging your N. America segments would be of benefit, but it's a consideration. If it were me I'd start on the west coast and move east if possible, e.g. LHR-YVR or LHR-LAX/SFO, in order to give the weather time to sort itself out over the Atlantic/Caribbean.

Second, AA has changed all its west coast < > Hawaii flights to use 757 aircraft. Most people find these planes to be fairly uncomfortable for long flights, even in first class (which your "D" ticket would earn.) On the other hand, AA flies 767s from Dallas and (re-starting soon) Chicago to Honolulu, so if you start juggling N. America, you might bear that in mind.

Third, Qantas' service from HNL to SYD is in rather dated aircraft (as of now - who knows what the case will be in a year?) and - again, just personal observation - I'd be inclined to skip over Hawaii and plan on a side trip somewhere "tropical" in Oz/NZ or Asia. Lord Howe Island? Northland (Bay of Islands etc.) on N. Island in NZ? Or while in California take a quick hop down to Baja California or Puerto Vallarta as a side trip outside the RTW. Anyway, just a thought.

As for a frequent flyer plan, BA is your obvious choice. You ought easily to achieve Silver status with this trip, which can be very beneficial in subsequent travel. There's a BA board on FT that you should visit anon.

Happy planning!