How can I export a report that has all transactions, and what account each transaction is assigned to?

Good morning, @davidmatyas.

Thanks for taking the time to reach out to the QuickBooks Community. How's your day so far? I hope all is well. 

I recommend using the Custom Transaction Detail Report for the data you're looking for. With this report, you can customize it to show all the info you have listed above. I'm including some steps below to walk you through running and customizing the report. 

Here's how: 

1. Go to the Reports menu. 
2. Select Custom Reports, then Transaction Detail. 
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3. A customization box will appear. Here you'll select the data you need. 
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4. Hit OK to run the report. 
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To Export the report:

1. Click on the Excel dropdown at the top of the report. 
2. Tap on Create new worksheet. 
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3. Hit Export. 
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That should do the trick. For more information about customizing reports, check out Customize Reports in QuickBooks Desktop. 

Please don't hesitate to let me know if you have any additional questions or concerns about this process. Have a good one!