Uh... farming mats for all that stuff and doing 100k honor per week on top of that isn't exactly fast, you know...
I would say:
- UBRS Jed+Rend farm runs - easy BIS trinket + decent boots
- Magistrate farm for the hat
- first boss DMN farm (if your group is very fast you can do 1st + 3rd, otherwise you'll run out of instance resets quickly) - wrist piece
- songstone of IF / eye of Orgrimmar - you can do the whole chain while leveling (you need Ony chain anyway and it's the same place), do the final quest when you hit lvl 60, single emp run, guaranteed BIS ring
- craft robe of winter night, that's cheap and you don't need to level tailoring
- honored AV for belt/cloak
- gloves are a bit of a problem but you can get dreamweave very quickly, they're cheap af and good enough (don't compare to gloves of power but you want speed, right)
- leggings - this sucks, there's basically no decent alternatives to skyshroud from LBRS
- 2nd trinket - get yourself an LBRS Wyrmthalak rush run, then finish the 2nd part (UBRS) when you're finishing Onyxia chain - free Eye of the Beast
- weapon - the fastest is buying staff of Jordan but you probably don't have the money right off the bat

DMN tribute staff is faster than Mind Carver + looking for an offhand
There. You can get it done in 3 days if you're lucky. No 20 hours of money grinding, no leveling up professions from scratch, no nothing.