You can setup a preferred dropship vendor for a product so that when you go to quick ship an order the system will auto select the dropship vendor account.
Go to: Management > Products and Suppliers > Catalog
On the product details page you will see a section called Preferred Delivery and Purchase.
Select Delivery Method of Drop Ship
Select the Drop Ship Provider Account you want to use
You're all set as this will now default as the preferred fulfilment method when you quick ship this product.