Assuming a person could keep up a hardcore schedule, I'd say it's possible to do it in a month, although I can honestly say I don't think it'll happen.

I know it doesn't answer your question exactly, but this is how I came up with that answer....

The first level 50's were appearing on the 3rd day, many appearing on the 6th. There are 8 fighting classes to level (lets assume that's what you meant). Assuming 5 days to the first level 50, you're looking at ~3 for the next 4 and 2 for the final 3..that's 23 days of non-stop leveling/grinding. Add some room for error, I got my month.

Now if you want to include the crafting and gathering jobs, you're looking at a lot longer. This is because crafting costs and you'd either need to grind for the money, gather all the materials yourself, or buy gil (which is against the TOS of course). I can't see anybody having all 19 at 50 anytime soon, even the 9 fighting jobs.