I'm in the process of purchasing a home and I called up to get my homeowners policy set up and they said since the furnace is the original one from 1965 they can't issue me a policy unless the burners have been replaced/updated.
Is it difficult to replace/update the burners on a Peerless gas furnace?
You should probably just plan on a new furnace. If what you said is correct, the furnace is almost fifty years old. Do you drive a car that's fifty years old? You should upgrade to a more efficient system (either wrap it into your mortgage, or have the sellers lower the sales price to cover it). I doubt that you can upgrade the burners on that furnace (how do you upgrade the carburetor on a Model-A Ford).
Good luck with your new home and please feel free to ask anymore questions.