Food permitted and prohibited in the light of Quran
ALLAH says in Quran: You shall not falsely declare with your tongues: "This is lawful, and that is forbidden," in order to ascribe false things to Allah, for those who forge lies against Allah will never prosper. (16:114)
So let Quran speak in respect to what food is Haram and Halal.
There are two types of food Veg and Non-Veg. 
Lets see what Quran speaks about Veg food.
1)	Vegetables and food-grains are HALAL. (78:15)
2)	Fruits and water is HALAL. (2:22)
So in short according to Quran all kind of vegetarian food is HALAL.

Lets see what Quran speaks about Non-Veg food.
1)	In non-veg 4 things are prohibited.  (2:173 & 16:145)
2)	In non-Veg permitted food (animals) are cattle/livestock. (5:1 &16:5 )
3)	Fish is permitted. (16:14)

Conclusion:   Quran tells us not to declare falsely any thing as haram or halal and attributing it to ALLAH. So we cannot say anything Haram which Quran doesn’t say neither can we say anything halal to which Quran doesn’t say.

Question:  So what is the ruling for these animals are they Haram or Halal for eg: Dog, cat, rat, lion, eagle, snake, lizard etc.
Answer:  We cannot say whether those animals are haram or halal (See 16:116). However Allah says to eat from which he had made lawful (See 2:168) and the food which Allah made lawful is being mentioned above. Allah knows best.