The adventure as stated in the book is meant to take the characters from level 1-7 however I actually pitched that back a bit with my current party (my second time of running this). I am DMing for a brand new group of players and wanted them to really get a feel for each level rather then have it a whistle stop tour, I also intended for this to be an intro and then transition into my own campaign.
What I have found is that it very much depends on party size, some of the encounters become exponentially easier with a larger party. My current party is 6 players and we are using the PHB and other source materials for character creation as opposed to restricting it to the limited rules that come in the set.
Therefore my rule of thumb for this is, if your party is 3 players or less follow the guidlines as given, 4 or more players then start considering a slower progression rate, it allows every player time to really get to grips with there skills and how the game flows without a jump ever few sessions.
The way I am therefore running this with my current party of 6 is 1 level after the first basic quest, then another level once the remaining 2 quests are completed but I give them more in terms of magic items and loot to find and put a small magical and curiosities store in the town. I also sprinkled a bit more in terms of enemies/traps/encounters through the adventures.
From there I try and judge level increases based on how I feel the party is progressing and getting a handle on things but certainly level 3 by the time they have completed the 3 beginner quests and one follow up quest.
That leaves 5 follow up quests which I found a party of 6 managed very easily so I levelled them up to level 5 as opposed to the suggested 6 over these quests. That meant killing the dragon ended them on level 6.
But like I say this is largely because, even with the additional traps and trickery I added throughout the adventure, my party of 6 would have found it far to easy at a slightly higher level in part because they where so well balanced as a group (sorcerer, Artificer, paladin, rogue, cleric and barbarian)
In terms of time, each of the beginner quests took about a 4 hour session each, we possibly could have powered through and completed 2 in a go but the players where really finding there feet with the game and I didn't want to rush them through.
The medium quests, depending on the quest in particular each took about 6-7 hours to complete but that was with extra description, roleplaying elements in between in the town, and as mentioned minor additions to each quest.
Fnally the dragon battle I find is a single session but, I split it into 2, one session getting to the dragon lair, with encounters and story added in, then the actual fight itself