If you have a 3-button key it will use a transponder chip for the immobiliser that cannot be copied. The transponder is pre-coded to suit the original car by Alfa and it cannot be altered. You cannot program your car to accept this transponder.
For the billionth time
only type 1 keys can be copied by high street key cutters. The old GTV for example. If you have any car from a 156 onwards then they can't do it as the transponder is locked and/or encrypted depending on type.
It is possible to make a clone if your car ECU is interrogated but this is a specialist job and you will have to travel to the person doing it (or post your ECU to them). Minirib can do this for code2 keys but I think your GT will be a code 3 which is even harder and I don't think anyone is doing this at the moment.
You have five choices:
1) Give up, don't waste any more money trying to take a short-cut and buy a key from the dealer. It's pricey but not as pricey as having no key at all.
2) Remove the immobiliser transponder from your one key and strap it to the ignition barrel. You have effectively overriden the immobiliser and you car can be stolen plus the insurers probably won't like it (unless you tell them it has no immobiliser), but it is a cheap solution.
3) Have the immobiliser function removed from your ECU - AlfaTuner on this forum - and add an aftermarket one
4) If you have a code2 key then Minirib can help (and a few others) but you do have to go visit them and pay them of course.
5) Get a replacement ECU from a scrapper with two keys.
If you want to know what immobiliser type you have look on the key blade. It will have a number stamped near the top of it. If it has a 3 then Alfa have you by the purse-strings I'm afraid, although be positive as they do this for a reason and the system they use does mean it is very hard for anyone to steal your car.
By the way, this transponder info is in no way linked to the remote alarm/locking functions. The circuit that controls this is separate and you can get your car coded to accept a second-hand circuit so long as you have the Alfa key code (which you can get from your dealer).