Yes! During each ferment, the mother scoby (the one you added) will produce a baby scoby.
Every scoby can be used four times before it gets too old and needs to be discarded. With each batch of kombucha a baby scoby is produced and the process starts again, you will have a fridge full of scobys before you know it.
To reculture:
You will need 300 mL (10 US fl oz) of brew from your previous batch along with a scoby. You do not need a whole scoby, if you want to make multiple batches you can cut a scoby in half and just use that. The important piece is ensuring you have 300 mL (10 US fl oz) of starter culture.