I don't think it'd be wrong to send her to the Anglican school.
It comes down to what you thunk is the best option for DD.

I went to Catholic school, DH is an atheist. DS goes to a private ecumenical school that doesnt teach religion but is based on judeo-Christian ethic. The other non govt. school I looked at was a Lutheran school. If we'd gone with a religious school, I really wouldn't have had an issue sending the boys to a school of a different denomination than Catholic. Anglican schools are by reputation very good and also seem to teach about all religions not just their own.
As far as zoning goes, schools often have a quota of out of zone students they can take. It varies from year to year, per school, depending howany kids in their zone they can take, and how many other kids the education dept specifically requests they take. If they have places left over then they cNntake kids outside their zone.

If you are interested in an out of zone school, enquire now. If they have a quota list and there's. Name they recognize on it, and they know you want to go there, there's a better chance of getting in