If the less than $2000 income was from W-2 wages, he does not need to file.
If the income is from other sources, he probably does need to file.
You do not report his/her income on your return. If it has to be reported, at all, it goes on his own return. Your dependent child must file a tax return for 2018 if he had any of the following:
1. Total income (wages, salaries, taxable scholarship etc.) of more than $12,000 ($6350 in 2017).
2. Unearned income (interest, dividends, capital gains) of more than $1050.
3. Unearned income over $350 and gross income of more than $1050
4. Household employee income (e.g. baby sitting, lawn mowing) over $2100 ($12.000 if under age 18)
5. Other self employment income over $400, including box 7 of a 1099-MISC
Even if he had less, he is allowed to file if he needs to get back income tax withholding. He cannot get back social security or Medicare tax withholding.
In TurboTax, he indicates that somebody else can claim him as a dependent, at the personal information section.