As far as I know, the only quest you need to do is Dragon Rising. It's the quest the Jarl of Whiterun sends you on with Irileth to kill the dragon at the Western Watchtower. Completing that quest should open up random dragon attacks. I don't believe there is any need to go further in the MQ.
I don't think the dragons that are "in the ground" in those inverted dome shaped bocci ball courts come out until a certain point in the MQ.
However, the game goes through dragons spurts. I only saw one dragon last week, real time. However, this weekend, I was tripping over them each time I started a game session. I even had 3 dragons in 3 fast travels in one session on Sunday.