Oh no! Hopefully, your neighbor will recover quickly with no complications. You may be covered—but a lot depends upon the particulars of your policy.
Let’s review renters insurance and dog bites:
The important thing at this point is to notify your insurer just in case your neighbor decides to take legal action against you. Unfortunately, if you are sued, your dog will be flagged as a liability, and your rates will likely go up.
Best wishes on dealing with this accident.