We had two female dogs (not Corgis) when I was a kid and they could not be in the same room together because they would fight. There ARE multi-female dog households, but here on MyCorgi when someone needs to rehome because two dogs hate each other and are fighting badly, it's almost always two females.
Lots of breeders (most of them) have multiple females, but it seems that homes with more than one female and a male or two as well manage better than just two girls in many cases. Not sure why that is, and it's just an observation, nothing scientific. Also, breeders will usually tell you stories of having to place a girl because two were fighting.
I don't know, personally I would not try it. My boy is fine with all dogs, but my girl frequently does not seem to like other females, even ones she sees regularly.
Here is a good past discussion for you on females vs males etc: http://www.mycorgi.com/forum/topics/advice-on-corgi-2
And here are a couple of others about singleton pups. Keep in mind that Frosty was singleton from birth. It might make a difference for your pup depending on how long the others in her litter survived. Hope this helps!
I have two girls and they get along great most of the time. They run and play all day and cuddle up together on the floor. They take turns cleaning each others faces and ears. However, Daisy, my oldest girl (only by 6 months) is definitely the boss and can be possessive. She does not like to share attention with my youngest girl Poppy. Daisy will not allow Poppy on the bed or couch if she has laid claim to the area first. But... if Poppy is on the couch or bed first then Daisy has no problem. They have some occasional fights... typically over food. Mostly growling and snipping at each other but nothing serious.