Is it wrong that I am happy even though I found out recently that my dog passed away? I am sad she's gone but I feel guilty to be going on with my life. :(

There is nothing wrong about being happy. There is nothing wrong with moving on faster than most people when a pet passes away. You are allowed and accepted to grieve as much as you need to. Your pet knows you will be okay and no matter what, you will never forget about them. You will be okay.

not at all, its very sad when you lose a dog they are such an important part fo your life but they would not want you to be upset and being sad every day they would rather you remember all your good times and smile about those instead

Loss is personal. Nobody can tell you if what you feel is right or wrong, because it isn't right or wrong to feel. It sounds like you have accepted that death is part of life, you have held onto the love you have for your dog, but are coping in a healthy enough way that you can go about your life. That's what works for you, so try to not think about it being right or wrong. There is a grey area we can grieve in. We all do what we have to do to get through the grieving process, and get back to our normal lives.