The Doctor is the last of his time-traveling species. He never dies, but "regenerates." Because he's been around so long, civilizations all over the galaxy know of him, and love him. He strives to maintain goodness and order in the galaxy. He does not delight in bloodshed, but tries to calm disorder peacefully.
His heart is big, as is his personality.
Jesus Christ was first, the literal son of God, but also the last prophet before the "great apostasy," of the hundreds of years when the authority to act in God's name was absent from the earth. He, too, was kind and loving to a degree that we will never fully be able to understand. Through He once physically died, he was then resurrected -- He lives, even today!
While science fiction has given us a "Doctor," we have the ultimate doctor, our Savior, Jesus Christ. He has promised us that He will never leave us, that He will always be with us. He said:
I will not leave you comfortless: I will come to you. Yet a little while, and the world seeth me no more; but ye see me: because I live, ye shall live also. At that day ye shall know that I am in my Father, and ye in me, and I in you. He that hath my commandments, and keepeth them, he it is that loveth me: and he that loveth me shall be loved of my Father, and I will love him, and will manifest myself to him. (John 14:18-21).
What a promise! And I know that it's true. I know that our Savior lives and loves us. I know that He truly will never leave us comfortless, but will come to us if we merely do our part (through prayer, scripture study, church attendance, and commandment keeping). He freely offers us that peace, and that peace will never end (unlike Doctor Who, which TV series will probably someday end, sorry).