Only through personal experience (in PA), I learned that:
A bank account, opened within 12 months prior to the person's death, is taxed 100%. I opened a new account for my parent in Feb and she died in Nov. We did this so we could do her banking closer to her home. This was a mistake.
It might be wiser for your Dad to make funeral arrangements NOW and pay the money directly to the Funeral Director NOW. Or, give YOU the money now for that purpose. Just keep it OUT OF THE BANK or, at the time of his death, GET IT OUT OF THE BANK immediately before anyone knows he died!!