The Travel Editor replies: You obviously need a round-the-world ticket, but you should choose these carefully if you wish to avoid incredibly long flights with frequent en route landings, long waits and untimely hours of arrival.
You are certainly not too late for January 2000. I have spoken to Trailfinders (tel: 0171-938 3939), one of the companies that specialises in putting together the kind of route you are talking about, and they inform me that it is only possible to book 11 months ahead anyway. What this means is that any fares quoted for the year 2000 are still provisional - they may yet be adjusted upwards - although you will be able to make your bookings in a couple of months' time.
You can arrange this trip to travel in either direction. One fare, which is routed first via the United States, costs pounds 1,596 including all taxes, "until further notice". This includes the expensive leg from Orkney to London via Aberdeen (which costs more than pounds 250) and there is no need to stay a night in either Aberdeen or London. The ticket would take you from Orkney to Heathrow to Los Angeles, where you could change for the short hop up to San Francisco, with no need to stop over in LA. This San Francisco leg could be omitted, although the saving would only be about pounds 60.
Resuming the journey at your leisure you could continue on to Rarotonga in the Cook Islands. From there you could continue to Auckland, then to Sydney, then to Singapore. Finally, you have the trip back to the UK on Singapore Airlines, which again looks quite convenient - arriving 5.50am in Heathrow, and connecting so as to arrive in Orkney by 10.35am on the same day.
Travelling around the world the other way might suit your purposes better if you wish to arrive in Auckland first. A route flying first from Orkney to Auckland, backtracking to Sydney, then continuing on to Rarotonga, San Francisco (via Los Angeles), Vancouver, London and back to Orkney, costs very slightly less than the previously option.
Another equally reputable company which could organise your travels is Bridge the World (tel: 0171-911 0900). Both companies can easily book your accommodation in Rarotonga.