I got my travel insurance from Columbus Travel. They charged about 28% extra for being diabetic. For other advice, suggest you look at these search results for 'travel' + 'diabetes':
http://www.google.co.uk/search?q=di...7SKPB_en&redir_esc=&ei=ZLfhULbqMYid0QXxq4GAAg
Imagine Thailand might be tougher than the other places. You will definitely need health insurance for the States. NZ and Australia might have some reciprocal arrangements with the UK, not sure.
You need to think about how long you are going away for, how much medication/strips/insulin/lancets, etc. you need for that period, then multiply it by half and add extra on in case of loss or damage in transit. Need to think about how you'll keep things cool (you can get special envelope things to keep insulin pens cool) and how you'll dispose of lancets/strips (small sandwich boxes work well for that). You can either take it all with you (take a prescription with name of your doctor and surgery on it and/or letter/card indicating you are insulin-dependent - I believe there's such a thing as an insulin passport you can get). Another option might be to have items posted to you for pick up - but not sure on rules for sending medication through post - and you'd have to allow additional time for it to arrive. As previous poster said, if you do carry everything with you, don't carry it all in one bag in case of loss/damage. And better not put insulin in hold baggage as it might freeze there.
Another piece of advice is to obtain the generic (standard) name for your medication as it may use a different name overseas.
Research and plan and discuss with your doctor/diabetic nurse - get what help you can. Enjoy your trip.
