No it's not informal. What you wrote is indeed correct. Removing it is done sometimes in spoken Arabic afaik but it's grammatically incorrect.
PS: A similar example is the French negation "ne ... pas" (like "don't do this" is "ne fais pas ça") where the "ne" is often omitted when speaking ("fais pas ça"). It's not proper French but it's how we speak in day to day life.