All of us will have different ideas on what we think is the better choice. IMO, a crate is better than being in a separate room - but that's totally dependent on how much room you have, your budget, etc. so I'm not criticizing your choice at all, just mentioning that IMO having her in a crate, where she can sit back and observe, would make her more comfortable than being confined alone.
GSDs can be extremely vocal, lol! She could just be a vocal one - so the whining could just be her personality. IME, being upbeat and confident helps them adjust. So instead of being, "Oh, what's wrong girl?" be more like, "Wow, you have alot of stories! You could write a book!"
I like playing with a new dog too, if you can find what she likes. One of my dogs had only ever played with tennis balls, so that's all he'd play with when I got him. They're all different, and it takes time to find what they like sometimes. Some might rather a rope toy. If you can find a toy she likes, this will help you bond.
Good luck with her! Thanks for giving her a loving home