Salut Josiane !
I backpacked alone Laos-Vietnam a few years ago, and had no problem with safety. It is pretty safe, you basically need to apply the usual rules such as not going out alone at night, etc. However I did go out alone at night a couple of times and had no trouble. As in Canada, it is a question of "good or bad luck"...
You will have nice weather in January
Dry and warm, not too sweaty.
Transport is slow and nerve wrecking, especially busses. They honk all the time (I mean every 30 seconds or so !), they stop in villages and along the road to pick up passengers, and despite the fact that they go way too fast for the condition of the roads, it takes forever to reach the destination. Count a
minimum of 2-3 hours per 100 km. Plus you often need to do some tuktuk in addition to the bus ride, before finally walking in your so well deserved hotel !
The experience is worth it though, for anyone willing to get a good sense of SEA.
How long are you planning on being there ? Because of the slow transport and the slow pace of travel you will certainly adopt after a few days (because that's what S.E.Asia does to any westerner), you better plan on staying a minimum of 10-15 days per country. If you want to visit Vietnam in its whole (north to south), you will need even more time.
Budget wise, I'd say an average of $15-$25 per day is feasable, including food, lodging and transport.
If you have more questions, please feel free to ask.