I figured this out on my own as Quickbooks has not solved the non-profit classes/funds issue. I also use Quickbooks for a church and use classes to track funds. I need to move amounts at the end of each month from the General Fund to the Mission's Fund. Everyone always says to use the General Journal but it always unbalances the classes. This is really frustrating and should be way easier.  So here's what you do. (It's putsy and doesn't make sense but has worked for me for years and years.)

-Create a Wash Account for the 4 transactions that you will need to do every time you move amounts from one class to another. All 4 transactions will have the same date and amount.

1. In the register of the Wash Account, enter a transaction with the amount in the Payment box, enter an Income Account, and enter the Class you want the money to go into.
2. Next, enter a transaction with the amount in the Deposit box, enter the same Income Account that you used in Step 1, and enter the same Class as Step 1.
3. Again, enter a transaction with the amount in the Deposit box, enter the same Income Account that you used in Step 1, and enter the same Class as Step 1.
4. NOW, enter a transaction with the amount in the Payment box, enter an Expense Account, and enter the Class you want the money to come out of.

The Wash Account should zero out. Go back to your Balance Sheet by Class and see if it looks right (be sure the date is on or after the date of your 4 transactions).

I hope this helps. I now love Quickbooks because I was able to figure this out. If I hadn't, I probably would have moved on to a more non-profit friendly software.