Dog Bite - Homeowners Insurance - Medical Bills

My 4 year old son was bitten in the face by a neighbor's dog in our yard last week. He had several puncture wounds and 2 serious "holes" on his face (1 in each cheek) that required surgery and a 2 day hospital stay. The owner of the dog came forward and filed a claim on his homeowners insurance. The insurance company states that they will be taking care of any medical bills that incurred. However, this dog has never had any vaccinations of any sort and there is still the possibility of future treatments such as possible rabies shots for my son and plastic surgery.
I do not know how to approach this matter, as we have health insurance and his medical bills are being paid through my insurance and also the possibility of more bills incurring in the future leaves me questioning what should I do and should I contact and retain a lawyer for this matter. I am not looking to "strike it rich" or anything I just want to make sure every right my son has is expressed.

How will this work with their homeowners insurance? Will they need to contact my health insurance company or is the money sent to me? Also what about future medical expenses? Also, do I need to pursue this further because the owner admits knowing the animal roamed freely and has not had any treatments from a veteranarian nor any vaccines in the past?

It is certainly possible you have a case based on what you say here; you should take a brief description of these events as well as your medical records to an injury attorney and see if the attorney thinks you have a claim; often you need to contact several attorneys to find one to take the case; the review of your case and records is often free and then they will normally take the case on a contingency fee basis if they think you can win; you would pay only if they collect for you...