Tax is charged on a cumulative basis. This basically means that in the second week, when she receives the double payment, she will get double the normal credits and rate band as the allowances from the first week weren't used. So, if she wasn't in the tax net in a normal week, she shouldn't be in the tax net receiving this double payment.
Although, she may pay more PRSI than usual. This shouldn't leave her out of pocket by much but the employer should be willing to address it on principle alone.