I was thinking the same but didn't want to confuse her with two names. Plus the spellings would be different so I'm not sure it would help much. I would rather have her focus on one brand and one name to print on her business cards etc....
Also, what would I do with two domains? Neither names would receive any type in traffic.
Is the dot com available for her first name + last name?
Yes it is, however that would be a difficult type and a long name. She has a unique first and last name.
Also: If I were to buy both domains, on which would you host the site on? Which domain looks better and more professional anyway?