Yes, overland possible and safe, though sometimes arduous. Make sure that you have your Vietnam visa already, either in Vientiane or beforehand. Assume no Vietnam visas on arrival at any land border you are likely to cross.

Preferably with a map in front of you, check out this thread.
Note particularly anything crossing northern parts, and the newest Tay Trang crossing near Dien Bien Phu (opened to intl's in 2007). The NaMaew-NamXoi crossing might be one to avoid--I've heard multiple tales of a nasty "transportation mafia" $$$$ticking it to foreign independent travelers heading INTO Vietnam from Laos at this location.

Suggestion: with a 6 week trip, you would be foolish to go to Laos and not get to Luang Prabang. If Vientiane (not much to see there) is your entry point to Laos, go overland up to Luang Prabang via Vang Vieng, then via Oudomxay to the Tay Trang border crossing and Dien Bien Phu. From there to Hanoi, or go to Sapa before going to Hanoi. It will be fairly cool to cold that time of year in the mountains of the north, esp at night. Between LP-Sapa, this routing gets you to more interesting, less touristed places and scenery...some of the better parts of Laos and Vietnam. Do a few hours of Google research on this to get the specifics and see if it might float your boat. Halong Bay overnight trip out of Hanoi is usually worthwhile, but weather that time of year may be cold and misty on the water, so check conditions once in Hanoi. If I had to stick a flight somewhere to save time, I'd be tempted to do a domestic Vietnam Airlines flight Hanoi-Hue, it skips over a whole lot of relatively boring parts of the country. From a base in Hue, you can go slightly north for a DMZ day motorcycle trip (if that interests you). Also proceed overland from there, to Hoi An and points south then on to Cambodia. This entire routing avoids backtracking. I would avoid dealing with routings involving needing double Vietnam entries, new visas, extensions, etc. Yes, it's doable but wastes time and money, and with proper planning the extra hassle isn't needed.

To save a day or so upfront, esp if you don't need/want to go through Bangkok, see if you can get SIN-VTE or LPQ flight directly. I wouldn't put the Thai train ride as one of the great Traveler's Experience of Asia...hmmm. With only 6 weeks, I'd say your plate is full with the 3 Indochina countries without adding any Thailand, assuming you want to stick with your India plans. And I wouldn't force/rush the rest of the trip to make landing in Sihanoukville for New Years Eve the priority. Frankly, the timing doesn't work out and from my calculations of your calendar, you'd best plan to spend New Years somewhere in S. Vietnam...HCM City could be a blast of a good time, maybe Nha Trang or Mui Ne if you must be at the beach (book lodging early though).