The minimum notice she must give is one week - that's the statutory notice period for an employee who has been employed for more than a month. She wouldn't be giving a week's notice as a 'courtesy' but out of a legal requirement as the minimum notice.
She does actually have a contract, albeit that she hasn't signed it. Technically she should give one month's notice as per her contract but there's very little an employer can do if the employee insists on only working one week instead of a month. It may affect any reference she gets in the future from this employer however. I'd be surprised, for instance, if her potential new employer wouldn't want a reference from the current employer, so she needs to be careful.
http://www.businessli...792628&type=RESOURCES