Dawnguard has a minimum level requirement of 10. I'd recommend waiting until 15-20 though since some of the quests are long and tough (lots of trekking through falmer infested territory). Hearthfire can be started at any time as its simply a material collection quest to build a house.

Should I do Dawnguard or main quest first?

Re: Which first: Main Quest or Dawnguard? It shouldn't really matter, regardless of which faction you choose in Dawnguard. (The two questlines meet at certain points, and those points are when you can mention being Dragonborn.) The most you get from are lines of dialogue where your character answers a question or two.

Do you have to beat Skyrim before playing Dawnguard?

You need the "dragon" elder scroll from the main quest to finish Dawnguard. I seem to recall being sent on quests to find all three Elder Scrolls during Dawnguard and was surprised I needed one later for the main quest.