You can say 我对狗过敏 -- wǒ duì gǒu guò mǐn
我 (wǒ) means I
对 xxx 过敏 (duì xxx guò mǐn) means allergic to xxx
狗 (gǒu) means dog or dogs

对狗过敏 (duì gǒu guò mǐn) means allergic to dogs

If you want to say that you are allergic to cats, you can say 我对猫过敏 (wǒ duì māo guò mǐn )
猫 (māo) means cat or cats