Your cousin's daughter is not technically your niece. She is your "first cousin once removed." The term "first cousin once removed" indicates that there is a one-generation difference between you and your cousin's daughter. In this case, she is one generation younger than you.
The term "niece" is reserved for your sibling's daughter or your spouse's sibling's daughter. Since your cousin is not your sibling, their daughter does not fall under the category of niece.