I have found numerous sources that attribute the quote "If we couldn't laugh we would all go insane" to Robert Frost but for the life of me, I cannot find when / where he actually said / wrote it.
You can't prove a negative, but I will (tentatively) declare
Frost didn't say that
As evidence, I present yearbooks.
No, seriously, my evidence is going to be mostly yearbooks here. High school/university students like cynical, smart-sounding, pithy, contrary, or otherwise amusing quotes to put next to their yearbook pictures. I guessed that they'd like this quote and went searching Internet Archive's text-contents storage to find some yearbooks with this quote.
As expected, a bunch of the results of the search were yearbooks. (Lots of yearbooks have been scanned into the archive, people like saving them). The earliest year with any results for the phrase was 1978, with 3 hits.
- Result 1: the 1978 Greensboro College yearbook. The phrase pops up in a rendition of the lyrics to the Jimmy Buffet song. The students must've really liked the music; the yearbook's title page is designed to be obviously reminiscent of the album cover.
- Result 2: the 1978 Columbia University Department of Nursing yearbook. Someone used this line as their yearbook quote, and attributed it to "J. Buffet".
- Result 3: the 1978 Wachusett Regional High School yearbook. Someone used this line as their yearbook quote, and attributed it to "J. B.".
All of that fits with young adults getting obsessed with a song and referencing the new cool lines it in their yearbooks. If the quote was from Frost, and around before then, I would expect students in prior years to have used this quote in their yearbooks.
To be more sure, I searched for this quote alongside "frost". This should pick up any archived version of the quote when it's attributed to Robert Frost. With a lot of false positives, annoyingly. All of the results attributing it to Frost were much more recent: 2015, 2011, 2010. (There was even one attributing it to James Taylor!)
This fits with @kimchi lover's comment (bolding by me, italics by them):
I agree with Joshua Engel: it's too dumb to be Frost. Google books didn't know of anybody writing this until about 2000, then Bill Watterson (author of Calvin and Hobbes) said something like it, then in about 2005 Buffet used it and in about 2010 people began attributing it to Frost.
If anyone can point to where Frost said this, I'd be happy to admit to being wrong, but seeing how long this question's been up I think that's unlikely.
Conclusion: as the snarky young adults can show us, this quote first showed up as a Jimmy Buffet lyric, and was only decades later misattributed to Robert Frost.