Is there a way to have the quantity automatically calculate if the item has a price and the employee enters a dollar amount on a sales receipt?

No

QB will enter the price per piece if you enter only the qty and total price, but that is all it will do

I will put in a Feedback request.  QBO fills in the price if you put in quantity and rate, it fills in rate if you put in quantity and price, but not quantity if you fill in rate and price.  Seems like that would be easy to add since they already have the other two in place.

Hello there, @Snowdenfarm.

As mentioned by Rustler, QuickBooks enters the price per piece if you enter the quantity and total price. Our closest alternative is to enter the quantity of the item instead of the price.

I'll send feedback to let our product team know how this feature helps your business.

For now, you can visit the QuickBooks Blog to check for new updates and features that we have. 

Let me know if there's anything else that I can assist you with. I'm always glad to help in any way I can.