To be honest, I don't remember it that well. Sure, I know Mirmulnir even though it wasn't particularly exciting as the guards did everything for me, but the next one? In my first playthrough I didn't encounter any random dragons until level 20 or so, and even then they were very rare. I couldn't understand why everyone else was complaining and calling them the new cliff races, I hardly ever saw any.
I'm pretty sure I killed my second dragon at Northwind Summit. I only know it because Aura Whisper was one of my first shouts, and the only shout I knew at the time that had to be learned from a wall in a dragon lair. My character wasn't a complete weakling at that point, she had spent a lot of time around Whiterun and Riften before she ventured further north. I must have killed it with a bow, as it was the only weapon my character used.
It's a little strange that I don't remember. I have vivid memories of other dragon encounteres: an elder dragon in the geyser area, my Khajiit's first dragon on the way down from High Hrothgar (he was like level 2 and had only Flames to protect himself with, it was terrible), an attack in Riverwood etc.