You didn't say where you came across that statement about capital gains. I think you are taking it out of context. For determining whether or not a dependent has to file a tax return, capital gains are unearned income, the same as interest, dividends, and distributions from mutual funds. It doesn't matter whether the gain is short-term or long-term. You just add up all the unearned income of any kind. If the total is more than $1,100 the dependent has to file. If it's $1,100 or less, the child does not have to file, regardless of the type of unearned income.
The statement that you quoted is not talking about whether or not the child has to file. If a child is required to file, and the child's only income is interest and dividends, there is an option in many cases for the parents to include the child's interest and dividend income on the parents' tax return instead of filing a separate tax return for the child. What the statement that you saw is saying is that if the child has capital gains, you do not have the option to report the child's income on the parents' return. But that's only a consideration if the child is required to file. If the child is not required to file, it doesn't matter whether the child's income could be reported on the parents' return because the child's income is not going to be reported anywhere.
Aside from filing requirements, if you are determined to sell the mutual fund, but there is no particular need to sell it right now, you should seriously consider waiting until you have held it for more than a year. Long-term gain is taxed at lower rates than other income, and the tax rate for long-term gain in the lowest bracket is 0%. If the gain is long-term there's a good chance that the child will not have to pay any tax on the gain at all. Even if there is some tax on the gain, the tax will be significantly less than if it were short-term gain.
