Hello there, @gretchen-bass.
There isn't a need to save your QuickBooks Online (QBO) company file to your computer since the program automatically back up your data. All transactions and changes you've made into your account is saved to the reliable Intuit system. You can learn more about this through this article: Do I need to back up my data with QuickBooks Online?.
On the other hand, the option to save your QBO data to a QBB file so you can import to Turbotax isn't an option. However, you can export lists (customers, employees, and vendors) and reports (General ledger, Profit and loss, Balance sheet, Trial balance, and Journal) to an Excel file through the Export feature from the Gear icon. Please see the screenshots below for your reference.
You can also look for a third-party application that can save your QBO data to QBB file. You can visit the QuickBooks Apps page to search for the best one.
Additionally, here's an article that'll further guide you in exporting your lists and reports. This way, you can easily download your data to your local hard drive. Fro the step-by-step guide, you can check out this article: Export reports, lists, and other data from QuickBooks Online. It also includes instruction about exporting non-posting transactions.
Please know that you're always welcome to comment below if you have other concerns or follow-up inquiries about managing your QBO data and transactions. I'm just around to help. Take care.