Keep in mind not merely the first verse of context, but the entire three verses that lead into the mention of Easter.
"Now about that time Herod the king stretched forth [his] hands to vex certain of the church. And he killed James the brother of John with the sword. And because he saw it pleased the Jews, he proceeded further to take Peter also. (Then were the days of unleavened bread.) And when he had apprehended him, he put [him] in prison, and delivered [him] to four quaternions of soldiers to keep him; intending after Easter to bring him forth to the people." Acts 12:1-4
Note the comment at the end of verse 3 in which the Word states, "These were the days of unleavened bread." Reflection on the context indicates that this could, honestly, go either way. Certainly it could and should be understood as a reference to the passover TIME. But one could easily make the argument in your favor that the REASON KJV translators would have gone with Easter is because Luke was a Gentile author with an understanding of the change in celebration.
The reason that latter argument doesn't hold a tremendous amount of weight is because Pascha does indeed get translated as Passover everywhere else. The first time we really GENUINELY begin to see Easter celebrated is in a post world where Christians have become blended with the political landscape and government of Rome. In Acts 12, the Christians have not even been named as Christians.
As we study out Easter's history (aside from this single use of it in the King James), we come to find out that Easter had its founding in the combination of Christian and pagan celebrations. If, in Acts 12, the Christians do not even exist yet, Easter most certainly cannot have weight as a blended holiday. For in that day, Easter was not a celebration of anyone. Thus, when Herod chose to apprehend Peter in chains, he opted to wait until after this day to bring about the charges.
Why? Why wait? Because Herod had a big celebration to attend? Not at all.
He waited out of respect for the Jews and THEIR holiday. Thus, it is indeed the Passover.
So to what end would we make the argument that Easter is an equally perfect word for this time? Only that Easter had its roots in the Passover period of Jewish tradition. It evolved into many things over the years, but in this particular time, one should absolutely understand that Easter, in Acts 12:4, is a reference to the Jewish Passover... not a pagan festival.
Whether one agrees that Easter is the best word to say that... we'd have to have a separate argument. :)