I think taking Ginger to the park for socialization and seeing who she likes best is a great idea. I agree that it comes down to individual dogs. I have 2 males and 1 female, Duke and Champ(f), and Chopper. Duke is almost 8, Champ is almost 6 and Chopper is almost 1. We definitely have a large difference in size here from 58-60 pounds to 3.5 pounds. Our dogs all get along great. But I know my dogs and I knew when getting the third one it really did not matter the sex as my other two had already established their order in the household and in the natural order of things the puppy would learn his. But neither of my large dogs are aggressively dominate in any way so I did not have to concern myself with females fighting or males going at each other or well lets say one of the big ones eating the small one. Duke, however, does not get along with my MILs dog at all. She is an aggressive dominate even though she lives in an only dog household. She loves Champ and she loves to play with Chopper but her and Duke just clash as they are both the dominate dog but they are opposite sexes. I say start getting her around other dogs and you will see her true personality whether she is submissive or the asserter and that will help you when looking to add another to your household.