The congregation sang the hymn "Ïn the Garden." at the end of the episode (The Collection, Season 3). Little House was set in the 1870-1880s, but C. Austin Miles (the hymn's writer) published the song in 1912, and was born in 1868. So the song was not around during the time frame of the show. (Unless Mr. Miles wrote it as a kid).
Alicia tells Mr. Hodgekiss that her puppy won't go to heaven, but in 'Remember Me, Part 1,' she asked her Ma if he would go to heaven when he died, and Mrs. Sanderson said yes. There is no reason for Alicia to believe her puppy won't go to heaven when she was previously told he would.