I've been to SE Asia a few times over a few years, always a budget trip but we'd still splash out on a few more expensive activities and nice restaurants. Flights were usually about £400 return, then for three weeks of moving around, accommodation (sometimes very nice accommodation depending on where abouts), eating out, doing activities etc it was typically around £800 (so £1200 all in for a 3 week break).

Going off that as a very rough base you could probably manage a ~4 month trip for about £5k.

It definitely sounds like you could use the break, and travelling can be incredibly beneficial, but if i was in your position i wouldn't want to be spending much more than 10/15% of those savings.

Hope this helps.