Can you get fired for giving a two weeks'notice?

Yes, you can get fired for giving a two weeks' notice. This doesn't necessarily mean you did anything wrong, employers just typically have the right to terminate your employment early so they don't have to pay you for the remaining two weeks.

This shouldn't impact your professional reputation for future roles, but it may impact your bank account if you were counting on being paid all the way through until you started your next job. So, be prepared for this to be a possibility so you can enjoy your two weeks off as much as possible.