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).
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.