You have to fight instead of your dog
You should not only be concerned about future fights between this cat and your dog, but also about your dog's trust in you.
As you are the alpha of your dog, it is your task to protect him from any fights and problems. If you do that, your dog will trust you if he has problems with other dogs. It will be easier for you to handle him if he gets in trouble or is afraid of somebody or something. If you don't protect him, he will start to fight on his own. So it is absolutely necessary that you fight with this cat instead of your dog.
This may not be easy because the cat may not accept you as somebody who makes the rules at the moment. You are new and it is her territory, so she may accept but not respect you. To change that, I have the following tips:
Be very attentive! Protect your dog from any fight. If you see the cat seeking him, make some hissing noise towards her and chase her away. Try to intervene before the fight starts. If that was not possible and she started a fight, immediately intervene, take her and chase her away.
If you see your dog starting to be aggressive towards the cat, do exactly the same the other way round.
Be friendly with the cat in every moment she is not aggressive with your dog. Stroke her and play with her the same way you do with your dog.
Sometimes it is possible that animals which don't like each other on first sight get close and become friends. But that is not always the case. It can be possible that your cat and your dog will accept each other when the humans are around but fight when they are on their own. Don't let them alone until you are sure that they really accept (or like) each other.
Even when you protect your puppy, you have to be as calm and non aggressive as possible. The cat protects her territory. That is a normal behaviour. Don't shout, don't hit her, just take her and let her go some meters away from the dog. She has to understand that she can do anything in her territory like before but that the dog is a taboo.
For the cat it is easier if your girlfriend helps you with this task. For your dog it is important, that you do it, too. Seems to be a team effort!