Anyone can take you to court with a lawsuit. That the dog bit the woman outside your property could be enough for a judge to grant at least a partially favorable outcome to her, depending on what she claims her loss was. Nevertheless, it is unlikely that the judge would throw out this suit as frivolous as some tangible harm to her can be easily evidenced. You can claim no foreknowledge of owning a dangerous animal, but such claims are not so effective in a lawsuit as they would be in a criminal trial to show intent to harm. So that means in a lawsuit, that the animal is known to be dangerous or not known to be dangerous is basically immaterial... only that harm was caused to her as a result of your actions or negligence are. Your own personal losses could be paid for by your homeowner's insurance or any other insurance with the respective coverage, but chances are neither will cover such an incident.
As for your dog being put down, I hope that it is not a possibility. If she has not gone to animal control authorities with it yet, then the chance is smaller and smaller as the days go by that they will react in this way.