Need a bit more details - looking to swap just the engine or the engine and transaxle from the 2001 car? What transaxle is in the 2001 car - 3-speed auto, 4-speed auto, 5-speed standard?
Assuming you are swapping both the engine and transaxle, as long as you swap over the electronics (ECM, wiring harness, etc.) - this is a doable swap. Many cases, owners have swapped in \"newer\" 1ZZ-FE engines to replace earlier ones with little to no issue. Fortunately, most of the hard parts - mounts, exhaust locations, etc. can be reused. So little to no fabrication is needed there.
If you are just swapping the engine from a car that had a 4-speed, would be a little more complicated, as there are interconnections between the engine and transaxle and ECM. It can still be done, but you\'ll need to get your hands on the factory service manual and be comfortable with rewiring the harness.
Another option is to swap in just the short block (everything from below the cylinder heads). In that case, the engines are nearly identical - so no need to swap the ECM or wiring harness. But this assumes that the rest of the original engine is in good running condition (ie, old engine was consuming a lot of motor oil).