Because it’s due to payroll, it’s a business expense. Even though it’s employee NI, it’s deducted from wages before being paid, and it’s then paid to HMRC by the business.
In terms of recording this, there’s a guide here on how to enter this info on QuickFile:
http://community.quickfile.co.uk/t/how-do-i-enter-payroll-paye-journals-and-entries/53/4?u=qfsupport