Suppose your kid (8 years old) decided to set up a neighborhood lemonade stand and by some freak occurrence managed to somehow make about $3,000. How does one manage the tax liability on that income? Is it counted toward the parents' income?
Operating a lemonade stand would count as self-employment, and if they earned more than $400 they would be required to file a tax return. In this case, the income is too low for there to be any income tax obligation, only a filing requirement due to self-employment income. The tax return would be theirs, but the parents would still claim the child as a dependent. If they are unable to file, the parents would file on their behalf, but it's still a return in their name, the income is not combined into their parents tax return.
Even though the question is in the context of earned income, it's important to note that unearned income (think passive income like interest/dividends) has separate rules and depending on the amounts can be included on the parents' return, or a portion of it can be taxed at the parents' tax rate even if filing a separate return for the child.
This actually happened to my brother. Started a Minecraft server at the age of 14 which became massive and netted him about 100k through donations in a year. He had to file it as personal income (my parents obviously helped him do it) and pay taxes on it himself.
After the clarifications to the question, noting that this is a child selling things on eBay, I'd be a bit more cautious about the tax implications.
In particular, eBay does not allow users under 18 to have accounts:
Because listings on eBay involve entering into a contract, we require all our members to be aged 18 years or older.
As such, it's possible that you, not your child, would be the one earning the income from the sales (see this article for example). That's not to say you couldn't arrange to "buy" the products from your child at full cost, minus shipping, or somesuch, but it's something to be aware of.
That aside, if a child does have earned income, that income would be reported just as any other income, assuming it's sufficient to require filling (> $6k).