In order to file as head of household, you must have a qualifying child, or a qualifying relative. Since your son earned less than $4,300, he is a qualifying relative, even though he's too old to be a qualifying child. Here's the IRS criteria for that:
https://apps.irs.gov/app/vita/content/globalmedia/table_2_dependency_exemption_relative_4012.pdf
Additional details on this can be found in IRS Publication 501.
Your son who has no income would not be required to file a return. However, if you claim him as a dependent, he is not eligible for the stimulus payment.
Nick K, EA
