Yes this is the birth record for Pehr, 10 Jan 1760 at Mårenäs. Father is Knut Jönsson (although I would not have deciphered Knut without knowing Pehr's surname). As for the mother's given name, my guess is Pernilla, although the P does not look like the other P's in the record and the l's look short. Hopefully someone with a more experienced eye will comment.
Good luck, Fred