Installing a complete TDI engine with electronics and all into an A1 chassis is not terribly difficult, but I don't want to sugar-coat you into getting the impression that it's a straightforward affair. The key is in the completeness of the parts and in the attention to detail.
I know of someone in SW Ontario, albeit a very capable VW tech, who is installing a TDI off a `98 Jetta (A3) into a Rabbit Pickup. I have seen both engine and recipient vehicle. There are plans of even installing the drive-by-wire accelerator pedal cluster and electronic instrument cluster from an A3 if memory serves. The key I was told is to install a late-model fuse panel (that part is more-or-less a bolt-in affair, and have the complete -- and I mean complete -- wiring harness off a donor vehicle. It looks like a darn boxful of snakes!
The physical issues, like fabrication of the engine mounts actually appear to be among the easier things to do for someone who knows what he's doing.
If after reading the above I have completely turned you off the idea of a TDI the way it was designed (electronics and all), take heart; I have heard of (but not seen in person), a few TDIs with mechanical pumps. One of these is in the UK, residing in an A2 Golf owned by a chap who has tuned it to the neighbourhood of 165+ hp, so you know the horsepower potential is there.
Simple answer is that a mechanical Bosch VE pump from practically any previous VW diesel engine (1.6 or 1.9) should work. The UK TDI if I recall is using a pump (or internals thereof hybridized into a VW unit -- I can't remember) off a European Ford Diesel van for greater fuel delivery).
As a long term project, a Rabbit TDI should be a rewarding and interesting one as it would mean a very unique car. But don't get the illusion that you would have a workeable, issue-free TDI Rabbit by a simple engine drop-in, even with a mechanical pump. You would certainly need a transmission, clutch and driveshafts along with the new engine as the torque and power of the TDI would likely mangle the stock counterparts currently in a Rabbit in no time.
The people whose brains you want to pick here in the forums are Diesel Dazzler, Diesel Des, TDI RS, GoFaster.