Personally I would do the following with her. Catch a male near where you found her. It may not be a "new" mutation so much as a previously undiscovered recessive gene. Grabbing a male from her locale increases your chances at least of getting a guy who *may* be het for this trait, since she probably has siblings and cousins running around somewhere.
Breed them together, even if you end up with all normals (which will probably be the case) you'll have a bunch of babies who, if this is a genetic recessive deal, will all be carriers for this trait. You could then take the offspring, pick a couple of nice males, and breed them to their sisters. If it is a simple recessive you should get some goldens out of this. You could even breed back one of her sons to her, and increase your chances for more goldens.
Personally I would do this and establish the nature of the gene (dominant or recessive etc) before mixing it with a bunch of other mutations. Once she has a bunch of babies, and you get some nice males down the road, that would be time to buy a load of nice carmels or whatever you want to test them with, and breed them with everything under the sun. You'll certainly have a market for the offspring!