There is a way but it'll take some patience. Right now, the new shoot is being entirely supported by the parent plant's root system. By next spring, it should have enough of it's own roots to allow you to cut the link to the parent plant. Leave it till next fall & you'll have enough of a root system to ensure survival after transplanting.

You could try accelerating the whole process (eg. follow the directions for lilac) but I don't think Fothergilla is as robust as some of the other suckering plants and survival could be an issue.

scratch around between the two.. and FIND out what going on under there ...

once you find out.. you can act accordingly ..

ken