Need help deciding on where to spend our time!

I am planning our honeymoon for September. We’ve settled on Thailand, specifically Koh Samui.

I have accumulated a decent amount of points that I was planning on using for this trip. All flights are business/first class so we will hopefully be able to rest on the major flights.

Currently the itinerary looks like this:

Day 1-2: Fly US to Doha land ~8:30pm
Day 3: Explore Doha
Day 4: Fly Doha to Bangkok land ~7:20pm
Day 5: Explore Bangkok
Day 6: Fly Bangkok to Koh Samui land ~3pm
Day 6-12: Stay at either Conrad or Banyan Tree (up for other suggestions, but would like to stay around $600/night or less with private pool and beach access)
Day 12-13: Fly Koh Samui to Bangkok to Doha (9hr layover) to US.

What changes would you make to this? Is it worth stopping in Doha or should we just do a layover and go on straight to Bangkok to spend an extra day?