No, you do not have to enter your child's income. In general, in 2020 the first $1,100 worth of a child's unearned income is tax-free. The next $1,100 is taxed at the child's income tax rate for 2020. Anything above $2,200, however, is taxed at the marginal tax rate of the parent(s), which usually is higher than the child's rate.
Here is an article with instructions on how to enter your child's PFD in TurboTax.
https://ttlc.intuit.com/community/entering-importing/help/where-do-i-enter-my-alaska-permanent-fund-...
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