Yes indeed her tax code should be 1100 not 1000 if her circumstances are normal.
Assuming it is 1100 and that she gets eight month’s salary in 2016-17 she will have gross pay of £11,333 (Just under £1.417 per calendar month). Income tax for the year will be payable on just £333 making a liability for the year of £67. That liability should not fall due until her gross pay exceeds £11,000, which will not be until she gets her pay next March.
If for some reason her tax code is 1000 (meaning she only has a personal allowance of £10,000) she will have to pay tax on £1,333. Tax due then would be £266. She should begin paying this next January when she should pay £33 followed by two months at £117 (I’ve rounded all these figures up to the nearest pound).
National Insurance is charged at 12% on amounts over £671 per month. NI is not levied on a cumulative basis like income tax is. (If she works just one month in a tax year the full NI is due on her pay). That amount due (12% of £1,417 minus £671 which is near enough £90) will be payable every month.