I am trying to convince myself to do so, I need some time frame so I can plan myself.
took me around 1 week for each prestige level doing casual pvp
Took me nearly 3 months to reach prestige 2. Should need about 2 months for the next 2.
Personally, it took me 20 days. There was this guy though that was a whole rank ahead of me, so he must have gotten his in 15 days or so. For the average player that won't rush/cheese it, assuming you do all daily tower/brawl world quests and win 3-4 BGs, it's gonna take 2-3 months.
Took me 2 months in which I do mainly pve, if you do RBG's and daily world quests it should be around the same.