:P Welcome to travelpunk.com !!!
Backpacking with your beloved in Asia is probably the best place. It is hot and romantic
, and there is also plenty to see and do. No matter what you decide, you'll have a wonderful time there.
Your ideas are good, but I think 3 weeks wouldn't be enough to enjoy your trip. It would be a race. Transportation is very very slow in Asia. You have to include in your schedule lots of time to change places. It becomes part of the adventure ! It took 24 hours from Savannaketh (Laos) to Huê (Vietnam), for a distance of around 200 km. The mountains, transits, and customs were among the difficulties I encountered on that road (plus road stops for construction, and even hidden opium stock unloaded from one bus in the middle of a forest !!!). So the simpler, the better.
Exploring Vietnam North to South ; looping in Cambodia-Thailand-Laos or Thailand-Burma; Malaysia-Bali ; South of India-Sri Lanka ; North of India-Nepal; excursion on the Mekong (Laos-Thailand-Cambodia-Vietnam) etc. Those are more realistic examples based on your suggestions.
From what I know, to enter Burma, you either fly there or take the long boat run from Thailand up. Worldwidemike has been there and could give you more hints than I.
Hope it has helped you a bit. Don't hesitate if you have more questions. We'll do our best for you.