I forgot to add, that you can move some of the gravel from your established tank to your cycling tank. That will help to seed the population of beneficial bacteria in the cycling tank.
As others have said, after the new filter has been running on your established tank for a couple weeks - then moving that filter to the cycling tank will speed things along even better. Just remember to keep feeding the bacteria as you've been doing.
I can't guarantee a time frame, but I would assume your cycle would be finished within one week after making that filter move. So - 3 weeks from when you started running the new filter on the established tank.
Of course, you'll want to keep checking water parameters until you're sure the cycle is finished. It's not necessary to check it everyday if there aren't any fish in the cycling tank, maybe every 2-3 days.