Is it permissible to say that God is not able to create another god like Him in attributes and powers, not out of incapability but out of His justice, in order to refute the شبهة (misconception/suspicion) that His will is to create a son for Himself?

Do not delve into matters of creed about which you are not proficient. Your statement, "Indeed, Allah Almighty does not create a god like Himself," is correct because that is among the impossibilities. The creed of Ahl al-Sunnah is that Allah is capable of all things, and everything possible falls under His power. As for that which is inherently impossible, such as "creating a likeness of Himself," it is not a real thing and its existence cannot be conceived, and therefore it does not fall under the generality of His saying, the Almighty: "Indeed, Allah is over all things competent." Avoid discussing these matters with mere personal opinion and be keen to adhere to the expressions of scholars, and beware of disputing with the false unless you possess sufficient knowledge to establish arguments and refute misconceptions.