Taking a break from writing the step by step for the legendary to do some quick breakdown of how long each step will take.
To get first set of daggers, you must kill three bosses and pickpocket Hagara, then wait 12 hours and complete the first series of quests to get the first 2 daggers. After that you start collecting the gems from the legendary clusters. From analysis of the PTR, there is no difference in drop rate from regular to heroic that we know of.
You need 333 gems in total and a single cluster drops 5-9 crystals from PTR reports. The clusters drop at a rate of 1 per boss on 10 man and 2 per boss on 25. Taking an average of 7 gems, that would require 48 gems or 48 kills on 10 man and 24 kills on 25.
For this collection step, assuming your raid is considerate and lets you finish your quest before killing Hagara and the group starts downing all 8 bosses per week, it will take approximately 7 weeks to get the next set of daggers on 10 man and only 4 weeks on 25.
The next collection step requires 60 gem clusters in total. This will require 60 kills on 10 man and 30 on 25 which works out to about 7 more weeks on 10 man and 4 more weeks on 25, if your raid lets you get the net set of daggers without killing the extra bosses on the week you get the second set.
Of course, after this set, you must then kill Deathwing to finish the quest, which if your raid let you get the extra kills after you turned in quests, should be still I’ll possible the same week you finish the cluster collection.
So in total, it will take 14 weeks on 10 man and 8 weeks on 25 man to finish the quest line and get your legendaries AT MINIMUM!!!
This translates to us seeing the first legendaries the week of January 17th for 25 and the week of February 28th for 10 man.