The Alaska PFD is not a credit, it's income.
You will receive a Form 1099-MISC for the PFD in January. It's not really a dividend, even though they call it that.
You can claim the child as a dependent even if you file a separate tax return for the child. You just have to make sure that on the child's tax return you check the box that indicates that the child can be claimed as a dependent.
The only advantage of reporting the child's income on your tax return is that it's a little less paperwork, but there are potentially significant disadvantages that can result in higher tax for both you and the child. Part of the child's income gets included in your Adjusted Gross Income (AGI). The higher AGI could reduce or eliminate certain deductions or credits that are limited or phased out based on AGI, including the Child Tax Credit and the Earned Income Credit (EIC). IRS Publication 929 has a long list of reasons that reporting the child's income on the parents' return could result in paying more tax. See "Effect of Making the Election" on page 11.
So you are probably better off, and certainly no worse off, filing a separate tax return for the child.
