Naturalization and CSI for student

[urmeli]

First of all sorry if this has been asked before, I have been reading for hours and am still unsure...

I hold dual citizenship - German by birth, UK through naturalisation since June 2019.

Now my daughter wants to apply for citizenship too. She is 18 and has lived in the UK with me since 2009. She got her Settlement Scheme confirmation in August 2019. She attended a UK school until June 2019 and has been a student at UK university since September 2019.
I assume she can apply for citizenship in August 2020 as she will have had the Settlement Scheme approval for 1 year?
The only documents she can submit are the same as for the Settlement Scheme: letters from primary and secondary school to confirm 10 years of full-time education, and about 6 months of payslips from a weekend job in 2019. Will this be sufficient for naturalisation too?
I am really worried about the CSI issue though. We have only now become aware that as a student she should now have CSI - lovely that the university does not tell them that!
As the qualifying period she applies with will not include her university time, will she still have to show CSI? I have been full-time self employed since 2009 and therefore needed no CSI, and I understand neither did my children because I was working.
I found the process difficult enough for myself, but trying to apply this all to someone who was minor during their qualifying period is impossibly vague...
Any help greatly appreciated!

[dogcat]

Should be fine as: you were a 'qualified person' and she was a direct family member.

[dogcat]

OT
Re universities, the staff is so incompetent it make my blood boil ...
As a part of my degree of all things I had to take a module of EU law and remember particular lecture concerning free movement of persons. We were told by the lecturer something to the tune of .. as long you're working or studying in the UK you're fine or otherwise authorities will be after you ...
No mention of exercising treaty rights, self sufficiency, CSI or what constitutes 'lawful residence' .
Totally lamentable.