New years isn't a huge local celebration. It is however a busy time with travellers. I would think you could book a train ticket easy enough but if you are picky on what train you want to be on and what kind of seat/berth then you would want to book as soon as possible. There are sites you can book train online if you are worried about it, will just cost a few a little more.
There are multiple trains that leave throughout the day so pick what works best for you.
Seat61.com/vietnam has good info on trains and vietnam-railway.com will allow you to purchase online although as mentioned costs more then if you buy them at the station.