The rear end will fit but the 2001 having disc brakes may be an issue but I am not sure. I do know that disc works on different pressure than drum brakes do. I put a master cylinder from a 2001 Suburban on my 97 Silverado. It firmed up the brake peddle. It is a popular swap, and I have had no issues due to the swap. Some people who do this, don't like it, but I find it works good on my truck. The pressure in these trucks, is controlled by the proportioning valve, and that valve is inside the ABS control box under the hood, where the brake lines go into. Another thing is that your 99 burb will be 5 lug and a 2001 will be 6 lug, so you will need to swap rims. My carrier bearings went out in my truck in 2012, while I was battling throat cancer ( cancer free sense Jan 2013). A friend of mine helped me rebuild my rear end. We pulled the axles, and the carrier. Then replaced the bearings. We had to have the carrier bearings pressed off of the carrier, and the new ones pressed back on. The axle shaft bearings we did in his shop, but is was hard to get the old bearings out, and we broke his slide hammer doing it, but we got it done. In the long run, you are better off rebuilding your rear end, because that way you have new parts. By changing the rear end, you are installing old parts, but it is your truck.