How do we set up accounts for Owner Equity?

To amplify @Greg_the_Geek 's correct answer,  just as you don't record transfers from your Savings Account to your Checking Account as a form of income or expense, you take the same approach with your business' Checking Account.  It's all "your" money that you move around as you wish, and it's all "your" income and expenses, whether it comes in a paycheck or in the form of business profits and losses.

Quicken has no overt "equity" Accounts you can access.   If you want that feature (sort of) but still want to use Quicken then I'd advise keeping the business' activity in a separate file and using offsetting balance sheet Accounts in the two files to record transfers between your personal file and the business file.