Breathing with their mouths open is a way for dogs to cool off, it's their internal Air conditioning system.... So she's not necessarily thirsty, just hot & cooling her body off.
Congratulations on your new dog, it sounds like you two are meant for each other since you started wanting a puppy and then suddenly your friend needs to give up theirs... Can't wait to see pictures, she sounds adoreable! What's her name? Do you keep the old name or give her your own?