Assuming you are from an A8 accession country, you arrived in January 2004 with a student visa and effectively switched to EEA status on 1 May 2004. The current EEA Immigration Regulations came into force on 30 April 2006- these do require Comprehensive Sickness Insurance for those exercising Treaty Rights as students. As I understand it- an immigration solicitor could confirm- time spent legally in the U.K. under the U.K. rules could count towards Permanent Residence under the EEA Regulations but only if otherwise meeting the requirements of the Regulations.
Based on this- it's not clear how you could have attained Permanent Residence before your daughter was born in April 2009 and as a result, it's likely to be simplest to register her as British using form MN1. (U.K. born child under 18 with a parent who has subsequently become a British citizen or settled).
https://www.gov.uk/government/publicati ... n-form-mn1
Regarding your younger child, if you can show you obtained PR before he or she was born it would be safest to use form NS to get him a Certificate of British Nationality Status which can then be used to apply for a British passport. Otherwise it would be necessary to register child as British using form MN1.
Does your PR documentation state the date on which you are considered to have become a Permanent Resident? Same applies to your husband. He may have become a Permanent Resident on a different date. Only one of you needs to show PR before April 2009 in order for your daughter to be automatically British.
This is not intended to be legal or professional advice in any jurisdiction.