Hello josh26,
I'm glad you've reached out for help with this. QuickBooks Online has tons of reports you can run, and many of them can be customized/filtered to fit your exact needs. I'll help point you in the right direction.
Based on your needs, I'd recommend running the Customer Contact List Report. To find it, click the Reports tab on the left navigation menu, and search for the title in the search bar. Once you've located the report, click the small Gear icon located to the right of the report title, and click Show More. Check off the box next to Billing Postal Code.
This will create a new column on your report showing your customer's postal code.
I hope this helps. If you have any other questions for me, please let me know.
Have a great day.