Can you confirm you are talking about tax year 2019 and that you didn't make a typo and mean 2018? Some things that matter here.
 - How old will the child be on Dec 31 of the tax year in question?
 - Does/Did the child live in your household for the entire year?
 - Does/did the child (not you) provide more than half of their "own" support?

Yes 2019, the child earned the income this year.  The child is 8. Yes the child lived in my house . No the child did not provide more than half of their support .

Basically, becuase if the age the child's earnings will not matter when you file your 2019 taxes next year. If the minor has more than $1,050 of investment income such as interest and/or dividends, then the child is required to file a tax return. If they have more than $12,000 of earned income, then they are required to file a return.
Now if they have less than the above amounts they don't need to file a return at all. However, if any taxes were withheld on the earnings, then the only reason they would file a return would be to get any withheld taxes refunded to them.
As far as you claiming the minor child as a dependent, so long as they do not provide more than half of their own support, you claim them and it's not an issue. I don't know many 8 year olds that provide more than half their own support. 🙂
Overall the important things is, if/when the minor does complete their return, they must select the option for "I can be claimed on someone else's return." Otherwise, you will not be able to claim them as a dependent on your return.

@Carl if the child has both earned and unearned income the rules get tricky rather fast.  If the child has a mix of earned and unearned income (investments, etc.) then they may be required to file if their income is as low as $1050, even if the investment part is less than $1050.

And then if this is self-employment income (modeling, for example) the child must file if their net income after expenses is more than $400.

A child's income earned from working is always reported on a tax return in the child's own name.  (Sometimes a child's investment income can be reported on a parent's return, but if they also had earned income, then all their income must be reported on their own return.)

This does not, by itself, change the status of the child as a dependent.  The usual rules still apply (age, residency, support).  If the child provides more than half their own support, then they can't be a dependent.  But money only counts as going to the child's support if it is actually applied to support.  For child model or actor, for example, if most of their earnings are placed in trust until they turn 18 (or older), then their money is not used for their support.