Yep you can absolutely use a piece of fabric! As II80 said cotton jersey is the stretchy one or you can also use muslin or angliese cotton if you live in a warmer climate. No need to hem although if you know anyone with an overlocker just to run round it for you it will last a lot longer.

Make sure when you purchase your fabric that there aren't any flaws, holes etc as these may tear under the pressure. And make sure you buy the whole 5m in the one go rather than 2x 2.5 metres as the pressure on the seam can cause problems when carrying a heavy bub.

Ditto what Limeslice said - lots of WAHM make there own and some places sell the fabric already cut for you too.