How do I send a payment/donation to...Quickly on a onetime basis?

Are you set up for online banking from Quicken? If you use Quicken's Quick Pay for payees which support it, that should take place pretty quickly. If you use Quicken's Check Pay, that can take awhile until the check is printed, mailed and received. If you use you bank's bill pay, that can also be fast depending whether the payment can be made by the bank electronically or requires a mailed check. Finally, if the payee has a website where you can enter a payment to your credit card or bank account, that is typically the fastest way to get a payment in the hands of a recipient. 

You should be doing credit cards differently...

You should set up an account in Quicken for your Amazon credit card. Then record (download or enter manually) every credit card transaction you make with the card as a separate transaction. The balance of the Amazon Card account in Quicken parallels your real-world Amazon card account. At the end of the month or billing cycle, you can reconcile your Quicken account against your credit card statement if you wish. When you pay the credit card bill, in Quicken your entry is a simple transaction in your checking account: a transfer to the Amazon card account — which again parallels the payment int he real world. There are no splits when you make the payment; the breakdown of your expenses has occurred when you entered each credit card transaction. 

There are lots of advantages to doing it this way. Your transactions are recorded on the date they occurred, not the date you paid the credit card bill. Any transaction can have a split, if the transaction needs to be split in multiple categories; Each transaction can have a QuickFill rule, so charges to repeat Payees can remember the categories you've assigned. You can see the running balance of the credit card account during the month. I hope you'll try doing it this way; it's really the way Quicken was built to be used.