The Doctor is a funny character. Through sheer coincidence, he always shows up in the midst of trouble and really messes with the villain's day. As a result, his reputation spans throughout time, and everything in the universe either loves him or fears him.
As wonderful as The Doctor is, he is pure fiction. But there are monsters in our world far scarier than any Dalek, cyber man, or Raxacoricofallapatorion. The devil is said to be like a roaring lion, seeking whom he may devour. But the Doctor cannot save you from him. So who can?
In James 2:19, we are told that even demons believe in Jesus, and they shudder. We see examples of this during His ministry. Matthew 8:28-34, Mark 5:1-20 and Luke 8:26-39 all describe what is presumably the same instance of two demoniacs. Upon seeing Jesus, these men, possessed by their Satanic tormentors, ran to Jesus and worshipped Him, begging Him not to torment them before the appointed time (when the demons will all be thrown into Hell).
As heroic as The Doctor is, his almost Pacifistic nature means he's more likely to beg for mercy than be begged. Every episode would be significantly shorter if his enemies were so afraid of him. But no demon will ever be protected by plot armor when facing Jesus. He is so powerful that even the mere sight of His human incarnation makes them panic. Even Satan, when he tempted Jesus, fled upon His command (Matthew 4:11).
Physical threats are not the only thing we have to fear from demons, however. They have a greater weapon: temptations and deceptions. It is these we need to be on the look out for. But the solution to these problems is still the same: Study the word of God and apply it faithfully. Scripture says the devil flees from those who resist him, submitting themselves to God (James 4:7). The king of demons is nothing compared to the King of kings, and the "god of this age" (2 Corinthians 4:3-4) will bow before the God of Heaven. It is sometimes said "the devil trembles when he sees the weakest saint upon his knees". Therefore, pray, submit yourself to God, and watch how great a cloud of dust the devil will kick up when he flees from you.