I need some quality backlinks related with pet site

Very nice site, you could do with getting a nice logo though, but ye its very professional, straight in with the content, I like it a lot.

What you need to do is go around all the directories finding pet related blogs and commenting on them, the second step for you then is to do some link exchanges, pet niche is very tough so link exchange, especially with lets say a dog one because then people will go to that one for dogs and yours for cats so definitely worth link exchanging.

Maybe do some article marketing, getting your voice heard on the big article directories will get you some traffic too.