I just ended up in an area that is very obviously the end of the game.

I immediately left because I have 2 areas left to explore, But I was wondering if i'll be shoved into NG+ after beating the game, or if I have a choice like DS2.

If I don't have a choice I'll put off finishing the game and get a good fill of PvP.

You choose when

As an addition, can I beat the game and be in a position to start the inevitable DLC? Vague spoilery stuff is ok, I suppose.

I just don't feel like playing 5 hours again and be stuck with NG+ DLC.

You have a choice, it asks you just like DS2. "Start journey 2" at bonfire you can do at anytime after the credits.

What the others have said. If you want, you can roll right into NG+, but the game will ask you if you want to.