I applied to my daughters school as an 'out of area' enrolment. I had an interview and explained that my friend who lived 'in area' was my dd's carer after school and her children attended the school also. The Principal was great about it.
I would have fibbed about moving if that didn't work though.
I'd pick up the enrolment forms and see what proof is required first, and maybe have a chat to the principal?