Does the Dhuhr prayer become void if I pray with a picture of a person in my pocket, knowing that I intended to burn it and dispose of it due to it containing an act of disobedience?

Your prayer is valid and not invalidated by carrying a picture in your pocket. However, it is disliked to carry anything with a picture on it during prayer, such as a ring, garment, or a coin (dinar or dirham) that has a picture on it.