If the income belongs to your child, then any return should be filed by (or on behalf of) your child. Since there expenses that would lower the income below the reporting threshold of $400 of net income, it is not required to file a return.
However, if the 1099 is issued to you and not to your child, then you need to account for it on your own Schedule C and issue the full amount to your child (and file a 1099 for the income paid to your child since it exceeds $600.)
Since your child's net income is under $400, there would be no obligation for your child to file a return . However, you should keep with your records information about both the income and expenses for at least six years in case of any IRS inquiry.
Going forward, if the income belongs to your child it is best to update the paperwork with YouTube so that any tax documents are issued to your child.
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