US, Rhode Island Nat Records. In both these images it lists the birthplace as

Lisa Kay Horlacher

P.Q., Canada. My understanding is this is the abbreviation for Quebec. Is this correct or should I just leave the initials?

https://www.familysearch.org/indexing/batch/b937f824-a9dc-47c2-be20-d6a7e6da2ef7

Áine Ní Donnghaile

Unless the project has specific instructions about abbreviations, the general indexing guideline is not to expand the abbreviation. Index what is written.

barbaragailsmith1

https://en.wikipedia.org/wiki/Sainte-Croix%2C_Quebec

Field Help says, "You should expand abbreviations or correct misspellings when you can tell what the abbreviation stands for or what the correction should be to the spelling. " (Notice the St is the same as Street abbreviation two lines down.)

erutherford

P.Q. is the abbreviation for Province of Quebec. I would index it as Province of Quebec, as the Field Help says to expand the abbreviation if you know it, and now you know it, because I took a few Western Civ classes in college. My history degree comes in handy once again! 🤣