I paid for an xbox gold subscription as the adult, but my child who has a separate account...

A child account should not need a separate gold membership as long as its associated with an adult "GOLD" account period !!! As long as only one profile can be used at a time if the adult logs in the child is signed out

Can you try the steps here to promote your child account to an adult one?

support.xbox.com/.../promote-child-account

Note that "Steps 6 to 9 apply only to accounts that are currently billed to a credit or debit card. If your account has a pre-paid subscription, go to step 10."

Steps 6 to 9 are about adding credit cards - only necessary if the current Gold subscription is paid for by credit/debit card.

Let us know how you get on.

Hi Dave,

Thanks for coming to the forums. We understand you are wanting to change adult account to a child account. Unfortunately, this is not possible as the birth date set on Xbox.com is set and is unable to be changed. We recommend

creating a separate child account. You can then set the adult account as
home console then the child account can share any subscription like gold or game pass. Also share any games you own.

Thanks,

Brad

As the family sharing option on the Xbox one is a little bit different to the option on the 360 it is definitely recommended the way you describe it. Set up the adult account and get it a gold subscription. Then set up the child account(s) and add them
to the family and all the family associated accounts are able to use the gold subscription as well as all the digital purchases of the parent/adult account. And of course you can also add another parent/adult account, too.

Only getting a gold subscription for the child account only works for the specific child account and will not be valid for the adult or other family associated accounts.

Nothing can be transferred between accounts. You can set the console as your Home console to share with your child. https://support.xbox.com/en-US/help/hardware-network/console/my-home-xbox