Mom/ You should bundle up. It's so cold outside. Don't skip breakfast, If you do, you will get old fast.

Daughter/ Mom, No worries.

In this situation, is "No worries" totally wrong?
Should it be "Don't worry!"?

Thanks in advance!

Question

Mom/ You should bundle up. It's so cold outside. Don't skip breakfast, If you do, you will get old fast.

Daughter/ Mom, No worries.

In this situation, is "No worries" totally wrong? 
Should it  be "Don't worry!"?

Thanks in advance!

Answer

'No worries'  is very informal, Australian English which has caught on in English speaking countries. Rather use 'Don't worry'.

Answer

I think you're overthinking it. People could use either one.

Answer

In my opinion, "Don't worry!" is correct in this situation and "no worries" is incorrect.

"Don't worry" is a response to when someone is worrying, and you think it is unnecessary (hence you tell them not to worry).

"No worries" is a response to when someone thinks they have done something wrong, and you are reassuring them that it is okay, that it's not a problem, etc.
Example:
A: "Sorry I am late!" -> '늦어서 미안합니다'
B: "No worries" -> '괜찮아요.' / '아무것도 아니에요'