I don't know when the earliest you can book, but to be safe why not call right away and check. It may be that you can already book (otherwise you'll find out exactly when you can).
Be sure to book the Round the World Tour and not the simply segway tour (only the 1 hour training part of the full tour).
Also, be sure to ask for a discount if you're entitled to it (AP holders, DVC, etc.)
the number to call from the UK is: 00-1-407-WDW-TOUR (00-1-407-939-8687)
I would call now. We did the segway tour on the 28th December last year and booked the tour in March of last year. The tour is great fun to do and I would love to do it again. Have fun.