She has been with you for a week. She is in a new environment, with humans she doesn't know and has no bond with. Spend time working with her, bonding, and just getting the house routine down before introducing a lot of new things. Some swear by the 2 week shut down
. As she settles in her new home, you will see more of her personality and temperament show. It can take a few weeks up to months for a rescued dog to show all of their quirks. During this time, locate a good
with GSD and working breeds. A second set of eyes on your dog and her actions will be invaluable in determining if this is excitement, FA or something else.
As for dog parks; many GSD just aren't candidates for them. Personally, I am not a fan of them simply because to many are just uncontrolled chaos and a set up for an fight/accident waiting to happen.
Congratulations on the new dog.... and thank you.