You can do part of what you want to do but it depends on the BA - Qatar joint venture
Yes you can book Qatar flights via the BA website provided that it is a codeshare flight with BA flight number and a BA 125.... issued ticket rather than a Qatar issued 157.... ticket.
If it is booked via BA.com with a 125.. ticket yes you can reduce the cost using Avios in the same way you can with flights on BA metal.
However as far as I know BA do not code share with Qatar UK to Bangkok as BA fly UK to BKK so don't want the competition. From mainland Europe departure points this may be different.
You can however book BA code share flights on Qatar metal from UK to other Thai airports including Chiang Mai, Phuket and Krabi. Also to various other locations covered by the BA Qatar joint venture. Thai domestic flights if required are usually cheap.
As far as departure point you can leave from any Qatar UK departure airport (LHR, LGW, EDI, CWL, BHX).
Thanks CWL. That is very useful to know.
Can I ask the question of how I can get BA.COM.to bring up qatar flight options. I did a quick check from amstersam last night and only gave me BA options. When putting the booking in, do I need to put via DOHA?
Thanks again.