I'd say do a quick test by submitting you design to cafepress. It's a good way to see how long it takes and if people start to buy your shirts you can look into getting it made afterwards for a lower cost!
What type of shirt? And what's one unit?
You'll have to give some more specific definitions here...and by the way I doubt most of the answerers frequenting this site will have deep insights into the garment manufacturing industry :-p
I'd try searching using Bing or Google with clothing keywords like "time to make one shirt factory" "assembly time one shirt China", etc.