I am sure this has been discussed but I am back after being away from Skyrim for a few months.

Will Dawnguard be too easy if I just continue to play it on my previous character? Should I create a new one before I start the Dawnguard questline?

Depends on your level. I was able to pass through Dawnguard with little trouble at close to level 50. I'd keep the same character if you feel it won't be too easy.

You can start the dlc right after you leave helgen as long as you know exactly where the cave is. Plus if you do the dlc from level 1 you get to 13-20 by just doing the dlc.

The random vampire attacks that trigger the DLC MQ are not supposed to start until you are level 10. So, if you start a new character just for this DLC, either build up 10 levels, or find the cave.

I made a new character, played it up to level 10 and then done the DLC. Wasn't too easy, nor was it too hard. I'd say create a new character with skills that will make the most out of the new items (for example, an archer or a paladin so you can use the crossbows, new armours and Restoration spells).

I haven't played Skyrim for months before the release of Dawnguard so for the sake of immersion, I made a new character.

The game itself at level 68 on master is really easy for me (the character I started from scratch with Dawnguard), so it can go either way. If you played it through high level, well it's just to play through the story line. The challenge may or may not be there.

Why not do both?