Hi there, @cmeigs.
Welcome to the Community. I can share the reason why you're unable to pull up the 943 form in QuickBooks Online (QBO).
Currently, you can only run and file 941 and 944 forms in QBO. The Form 943 (Employer's Annual Tax Return for Agricultural Employees) is only available when using the Desktop version.
As a suggestion, you can manually file your 943 through the IRS website. Please refer to the links below for your guide.
Meanwhile, I've already sent a product suggestion about adding the 943 form in QuickBooks Online. I suggest you do the same request to have more votes. You can post your idea in this link: QuickBooks Online Feature Requests.
For your Unemployment Insurance setup, I suggest getting in touch with your state agency for validation of the information you've entered.
That's it. Keep me posted if you have other form or payroll questions. I'd be happy to help you further. Wishing you all the best!