It would certainly work for me in the context of a child starting school and being anxious to appear suitably dressed for the occasion.
But it's an odd way to ask your employer if they have a dress code, which I suspect is the OP's underlying reason for wanting to know this. A good employer would have given you useful information such as this beforehand, but assuming that in this case they haven't, then "Do you have a dress code/Is there a dress code?" would be a reasonable way to ask.
I'm not saying that asking about the dress code is wrong, because the suggestion is good. However, there is a difference between a "dress code", and what is typically worn at a particular workplace. Where I work, if you ask about a dress code, you'd get a list of a half-dozen things that are forbidden (ripped or dirty clothes, shirts with objectionable content, revealing clothing, etc.). But that wouldn't help you understand if you should wear a suit, or golf shirt and khakis; a business-type skirt or capris.
I really can't see anyone, apart from the insufferable grammar pedants found here (self included) who would hear "what should I wear on my first day" to mean "I only want to know what to wear on my first day, and no other time after that".