Changing incorrect age of Child on Family Sharing

Yes that seems to be correct. I missed the line at the top of that page about under-13s accounts need to contact support.*

Go to the Products support page and select Apple ID. Then follow the options. I didn't see one specifically for charged birthdates for children so 'Other Apple ID topics' is probably the best one.

After that I recall you will get the options of call or message.

Have all your credentials ready both for the organiser of the family group and the account with the birthdate you want to change.

*It's been some time since I had an under 13 in the family 😃

Update the date of birth associated with your Apple ID tells you how to achieve this:

To change a date of birth to any age below 13,* you must be a member of a Family Sharing group, and your family organiser must approve the change. ..

Follow the steps in the document to sign into the 'child' account either on the web or an iOS device, navigate to the option to change birthday, then 

1. Update the date of birth.
2. Follow the onscreen steps to send an email request to your family organiser.
3. Your family organiser will get an email with instructions on how to approve the request. 

No worries. I'd be interested in your experience in how this turned out for you. Be sure to drop back and report. Lots of people have this issue and it might help them too!