Good day, lj-ywca.

I'd love to help you find the 941 and State Unemployment reports in QuickBooks Online Payroll Core. Both reports can be found on your Payroll Settings.

Here's how to locate the Federal 941: 

1. Go to the Gear icon and choose Payroll Settings.
   
2. Click the Pencil icon for Federal tax.
   
3. From the Company Federal Tax Information, fill in the information. Then, click OK.
   

Here's how to locate the State Unemployment report:

1. Go to the Gear icon and choose Payroll Settings.
2. Choose the State name tax (sample screenshot shows California tax). Then click the Pencil icon beside it.
   
3. From the State Tax Information, fill in the necessary information and click OK.
   

Check out this article to be  more familiar with using the QBO Payroll Core:

• See what you can get with QuickBooks Online Payroll Core
• New and improved QuickBooks Online Payroll lineup

Let me know if you have additional questions about this, or need further assistance. I'm here to help. Have a lovely day!