The code is the same but you need to reconfirm every 3 months that you still qualify. They email you and it only takes a minute on the online system. Speak to your nursery or child care about when they need the code. But no harm on giving it to them now.
If you got your code in August you will have to reconfirm your details with HMRC in November or it won't be valid in January. And then every 3 months after. The code will stay the same unless you have been issued a temporary code (which start with 11).