Will a 2006 ram 1500 disc brake rear end fit on a 2001 ram 1500?

Have a look-see at these two places, I will put one here and the other in another window to make it easy to hyperlink/ http://www.circletracksupply.com/rear-disc-brake-conversion-kits-for-dodge-trucks.html

You are talking $750/ http://www.summitracing.com/search/part-type/disc-brake-kits/make/dodge/model/ram-1500

But after all that, geez, I had not paid attention to your real question, to use the axle/brakes from a 2006 and put them on your 2001. The 2001 has a 3:21 final. The 2006 could be either 3:73 or 4:10. The U-Bolts between '01 and '06 are also different.The conversion is the best way to go, all that stuff on top if you really want disc brakes. THAT is why in the image it shows the old axle, and the bottom line in answer to your real question is no, it wont swap Click the image for a nice full screen, and how the old parking brake cable is used

this is a 1996 with a 2006 disc brake rear end

yes with a flip kit