Well you've come to it quite late as you will be applying soon. It depends on how oversubscribed the school is. As PP say you can still hope for a non faith place. Try prayer
! (Sorry I actually meant that but it sounds flippant).
Catholic baptism isn't an option but it's good she is already baptised. I'd keep going to church regularly, speak to the priest, mention that you've moved area
ask about getting involved in the community. Could you read at mass? Or hand round the collection? Or help with the SVP? I wouldn't mention your dd and getting into the school to him now.
Not being too cynical here but if you are involved in the community it would be useful to get the priest onside for a recommendation if it ends up at appeal. At which point you can explain that family pressure meant you got a CofE Baptism but that you've been raising her Catholic and you want her in the school to support that.
One thing you could ask him is what happens about first Holy communion if she isn't baptised Catholic.
Hopefully he will be disposed to help in an appeal based on your regular attendance and being genuinely involved.
What are secondary options where you are? It's worth thinking longer term if you also want a shot at secondary Catholic schools.
I think anything that brings you back to church and more in touch with your faith is a good thing. People scoff here but at the end of the day you couldn't do regular church attendance just to get into school without faith. You must be getting something out of mass.
I love my dcs Catholic school. They do claas mass in school time, FHC with their whole class is a great time in their lives, we have lovely Easter and Christmas events, we have school masses that parents can attend (kids are so cute reading budding prayers and saying hail Mary etc,), Ash Wednesday and lent is a real thing in the school, we have a great community at mass and in school. Also, now I'm looking at secondary I have some great options outside of grammar and other people I know are looking at private or dreading the alternative if their dc fail 11 plus because they can't or won't look at the Catholic schools.
The best thing has been putting me back in touch with my faith. Your dd will have to make up her own mind one day but you have an opportunity to deal with your own beliefs now.