For 2024 kiddie tax only applies if the child has investment income over $2,600, so your son will not be subject to kiddie tax. All of his income will be taxed at his rates. If kiddie tax did apply, investment income over $2,600 would be taxed at your rates. The kiddie tax would be calculated on Form 8615. But there will be no Form 8615 in your son's tax return, since the kiddie tax does not apply.
Kiddie tax does not make any of the income tax-free. When people say that the first $1,300 of the child's income is tax-free they are assuming that the child has only investment income and no earned income. In that case his standard deduction would be $1,300. But your son has $11,000 of earned income. If his earned income is exactly $11,000 his standard deduction will be $11,450. So $450 of his investment income will be tax-free. The rest will be taxed at his rates.
You didn't say what kind of dividends he has, or whether any of the capital gains are long-term. There are special lower tax rates for qualified dividends and long-term capital gain. Because of your son's low total income, any qualified dividends or long-term capital gain that he has will be taxed at a 0% rate. But that has nothing to do with kiddie tax.
You must have gotten the $1,050 figure from some old information from 2018 or earlier.
