A dog that followed me home hasnt left. can i keep it?

[Kate M]

No, you can't just keep her. If the owner comes forward, you have basically stolen their dog.
Since there are only a few houses around, go ask the people there if they know the dog. Take a photo of the dog with you if you don't want to take the dog. Take flyers if people are not home. Not everyone looks online, so that can't be the only place you post.
If there is animal control, you do need to report her as found. You might be able to hold onto her until an owner comes forward, but you might not. See if you can post flyers in local vets, pet stores, feed stores and other local businesses.
If you did want to keep her, you need to do it legally. If there is animal control, they have a set hold period for an owner to come forward. After that, the dog becomes their property and they can then adopt them out, euthanize them, or transfer them to another rescue. Most will let you adopt once the hold period is up (you will have to do any paperwork still).