While the quill diameter of a stem made to fit a 1-1/8" headset and fork is indeed 1" (25.4 mm) in diameter, it will be called a "1-1/8" quill stem" so that's what you should ask for at your bike shop.

If you ask for a 1" quill stem you will get one to fit a 1" steerer and headset and it will be too small with an actual diameter of 22.2 mm.