Emily is a lovely name, but it's so common.
Carissa is nice as well.
Carissa Emily Harmon would be a nice combo. I really think that you should use
Emily as a middle name rather than a first name. Your daughter will probably thank you for naming her
Carissa rather than
Emily since
Emily has been the number one name for girls for the past decade. If you go with
Emily, she will probably get tired of being referred to as
Emily H. since there's a very high chance that she will share her name with at least one other classmate. I speak from experience.
My parents gave me the most popular name for girls during the year I was born, and I hated being referred to as
Jessica M. It was also very confusing because everytime someone said my name, I wasn't sure if they were addressing me or another
Jessica.
Carissa Emily Harmon would be a nice combo. I really think that you should use
Emily as a middle name rather than a first name.