Ok, the symbol is not backwards but it does just mean "dog". Year of the Dog is NOT a different character all together. So all you need to do is add the other character and it will be fine.
No, it's not backwards. Why would you lie about something like that? But it doesn't mean "year of the dog" either. It just means "dog." The character for "year of the dog" is completely different. Also, this character has one extra stroke.