This is just what I have found and have colected. Please feel free to forrect me in the comments with YOU'R OWN FINDINGS! :D

This is also a partial list. I will add more later.

Plant fats

• 
  Sunflower Seeds
• Oilyberries
  
• desert olives
  

Plant Proteins

• Ground Pear
• 
  Sunflower Seeds
• 
  Soybeans

Plant Carbohydrates

• 
  Sunflower Seeds
• Wheat
  

Animal Fats

• spotted Tapir
• red stripe salmon

Animal Proteins

• 
  Blue-Crested Pheasant
• tropical quail
  

Animal Carbohydrates

• honeybag ants
  

This is what I found:

desert
redstripe salmon: Animal Fat
sea lettuce: Plant Proteins

savannah
soy beans: Plant Proteins
sorghum: plant carbohydrates
Honey: Animal Carbohydrates
Spotted pig: animal fat
Sunflower Seeds: plant fats

Tundra: 

Polar Salmon gives Animal Carbohydrates, Animal Fats, and Animal Proteins. Yes, all three, and each unit of Polar Salmon gives one of each. 

How do I feed my pets

Your pets are fed automatically every midnight rollover, either with the petfood you've collected or with some of your silver.