Yes I am aware your question is relating to employment in Dubai.
Generally if a labour contract is for an unlimited period and a person has completed the minimum period of service, which is one continuous year, fixed by the labour law - then in the notice period is one month's notice, in accordance with Article No. 117 of the UAE Labour Law which considers such a period of notice obligatory for both the employee and the employer.
However, your daughters position is slightly different in that she is currently on probation. If the contract stipulates one week notice period during the 3 month probation for the employer and is silent for the employee, it is standard to be the same. Should you daughter wish to resign she really should approach her employers and have them confirm the notice period during probation is 1 week.
The employers is also generally obliged to pay the travel costs of a non UAE employee to repatriate your daughter back to her home country. But if your daughter resigns she may be liable to pay her own transport costs.
Another thing for your daughter to consider is that there is a mandatory ban is imposed upon onshore non-UAE national employees, upon the termination of their employment, preventing them from taking up employment within the UAE for 6 months - in the absence of a no-objection certificate from the employer. A 1 year ban can be imposed if the employee resigns and is in breach of their Contract (eg. giving insufficient notice).
Finally, your daughters sponsorship will be cancelled as her employer is under a duty to notify the Labour Department on the termination of an employee's employment, to allow the employee's residence visa and work permit to be cancelled. Employers should do so within 2 days of the termination. Following termination of employment, the employee (your daughter) will have 30 days to leave the UAE or find alternative employment.
Is your daughter intended on returning to UK or staying in UAE? If she wishes to stay, then I would advise that she either tries to make a go of her employment or be as amicable as possible with her employer, i.e. by at least offering to work more than the stipulated notice period to assist (for example).
I hope this helps. Should you require further information, please click accept and I will be happy to continue this dialogue.