Happy to help look into some options with you. Have you run a search for QuickBooks on our Shopify App Store? This will be the easiest way to find some integration options for your store. Here are some suggestions for you:
Each of these have a free plan available. Some have maximum conditions where you may need to upgrade to a paid plan, depending on the number of orders. For example, QuickBooks Sync by Bold is free for up to 30 orders per month. Choosing an app that works for you will depend on the needs of your business. If you are looking for something more robust than the options listed, or the features available on their free plans, you may require a paid app.
There is also a previous Community topic about integrating QuickBooks and Shopify that I will share here for further information. Other users simply suggest exporting your orders from Shopify, and importing them into QuickBooks manually for a free option.
Let us know what you decide!