I just rerolled to a DK last month actually, and am nearly caught up in the legendary quest chain. That will be your biggest issue, but the length between the new quests is so long you do have time to catch up eventually. Yeah, gear is totally random.. I'm the only plate tank/plate dps in my raid and the stuff drops so much we are disenchanting it at this point, as well has vanq tokens. it's all luck
I geared a DK alt over the course of ~7-8 weeks (took a 2 week hiatus recently) from lvl 85 in FL gear to 490 DW Frost with a 480 Blood OS. Rerolling to her in 5.2 from my old Warr main of like, 4-5 years, who is 494/488 for DPS/tank.
GOLD, LOTS OF GOLD. Buy a non good BoE (476), put in bags, cheese LFR iLvl, resell BoE for profit after you get lfr ilvl without it(the world drops work best for resale). Get a DMC, the two 496 armor pieces, and maybe the HoF bracers BoE.
CONQUEST GEAR. Buy 2s wins for 150g or whatever each, get 1800 conq, buy a damn good armor piece that's a huge ilvl increase. Takes 30 mins once you don't go splat, maybe 1.5 hours a week when you are freshly dinged.
DO LFR/DAILIES. Plan what VP you're spending on what - don't spend VP on a piece that can be replaced by LFR armor from 5.0, or is easily obtained once you can enter Throne.
I was able to get raid ready in a very short time over break and even got a N Sha touched weapon for what was going to just be an alt at the time.
Don't see why not, if you're not getting a new raid team together and some are still leveling, that gives you plenty of time to get ready. And really, you could probably get away with not being fully heroic geared if you don't get lucky with a few drops.
As others have said, 5.2 pending probably makes this the best time to change mains.
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