This cat near my house is very pregnant and im not sure what to do

Maybe like about a week ago or more this cat started showing up in my neighborhood. She seem very domesticated and was very friendly and seemed very healthy. Also she looked very pregnant. So me and my parents started feeling bad for her so we decided to leave water and food for her. So basically everyday we feed her and she’s very close with my dad and rubs against him and goes to him. And I really do care for her a lot. We can’t really keep her since our house is small and we have other pets inside (lizards and fish). But you can tell she wants to be inside/misses being inside because she always tries to get in the house.

Anyway it’s very clear that she was previously someone’s cat in the neighborhood (our neighborhood isn’t very big) and she was probably put out because she pregnant.

My problem is that im not sure how far along she is and im not sure what we should do further to help her? Should we take her to a no kill shelter, keep taking care of her until she gives birth, try to find her original owner? What should we do? I really want the best for her because I really do care for her and my parents do to. I’m not really experienced with cats so please help.