No, a tax return does not need to be filed for the $1090 capital gains income. The limit of unearned income for a minor is $1,100 as noted in the post by Bsch4477 below. The income is below the threshold for filing and you do not need to file a return for your minor child.
[Edited 02/27/22|4:17 PM PST]
@raybeyond
@Bsch4477
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