Doc is immortal and as such will not be aging. (But he'll be checking his mustache for grey hairs anyway.)
That being said, I am open to other characters trying to (and maybe succeeding at) stealing years off of his life. If you have a super creative idea of how to do that (and if you can help me come up with an evil reaction Doc would have to this life threat,) let me know! I'm really excited about the possibilities with this plot.
I'm also not opposed to his death during this plot, as long as it makes sense, offers the opportunity for character development, and causes conflict that can continue into later plots.