Sorry, mmbsr, but we can assure you outside of shooting soda cans at 100 feet not yards a 9mm carbine is just a nice toy and not very practical. There are millions of parts for 5.56/223 ARs out there but I am not sure where you would find parts for a 9mm lower.
If it has to be a 9mm carbine, I would recommend the CX4 even though they are no longer made. Or a Kel-Tec Sub-2000.
http://www.keltecweapons.com/our-guns/rifles/sub-2000/
It would be cheaper than building your own.
Jim