Is there a prohibition to take care of dogs in the rule in Islam, because I just to know it is haram if exposed to saliva alone?
It is only Haram to have a dog if it is for being a pet, other than that the dog is ok.
مَنِ اتَّخَذَ كَلْبًا إِلاَّ كَلْبَ مَاشِيَةٍ أَوْ صَيْدٍ أَوْ زَرْعٍ انْتَقَصَ مِنْ أَجْرِهِ كُلَّ يَوْمٍ قِيرَاطٌ
That the Messenger of Allah () said: "Whoever acquires a dog - with the exception of a dog to guard livestock, a hunting dog, or a farm dog - each day a Qirat is deducted from his reward.
But it is also good to take care of animals, and dogs are animals and there is a reward for taking care of animals.
Yahya related to me from Malik from Sumayy, the mawla of Abu Bakr from Abu Salih as-Samman from Abu Hurayra that the Messenger of Allah, may Allah bless him and grant him peace, said, "A man was walking on a road when he became very thirsty. He found a well and went into it and drank and came out. There was a dog panting and eating earth out of thirst. The man said, 'This dog has become as thirsty as I was.' He went down into the well and filled his shoe and then held it in his mouth until he climbed out and gave the dog water to drink. Allah thanked him for it and forgave him." They said, "Messenger of Allah, do we have a reward for taking care of beasts?" He said, "There is a reward for every one with a moist liver."
Some hadith's in this reference:
1] [Hadith - Bukhari 3:515]
A dog for guarding the cattle or hunting
Allah's Apostle(P.B.U.H) said, "Whoever keeps a dog, one Qirat of the reward of his good deeds is deducted daily, unless the dog is used for guarding a farm or cattle." Abu Huraira (in another narration) said from the Prophet, "unless it is used for guarding sheep or farms, or for hunting." Narrated Abu Hazim from Abu Huraira: The Prophet said, "A dog for guarding cattle or for hunting."
2] [Hadith - Bukhari 3:515]
Angels Don't enter
I heard Allah's Apostle(P.B.U.H) saying; "Angels (of Mercy) do not enter a house wherein there is a dog or a picture of a living creature (a human being or an animal)."