This cracked me up when I first saw it - it's a few years old, from the episode when Quagmire moves in with the Griffins. They want him to move out,and Peter says something like," I can't toss him on the street like a prom night dumpster baby" that leads into the clip.
Some people come into our lives and quietly go, others stay a while, and leave footprints on our heart, and we are never the same.
The only thing this and the original song have in common is the "I'm Just a __________ Baby" part. The melody, harmony, rhythm and rhyme scheme are all different ...
I definitely get what husk means with the first few lines. I take it as a nod to "Broadway Baby."
"Some people can thrive and bloom living life in a living room, that's perfect for some people of one hundred and five. But I at least gotta try, when I think of all the sights that I gotta see, all the places I gotta play, all the things that I gotta be at"
Family Guy does this all the time - makes allusions to songs, but changing it up so there's no copyright infringement. Yes, it's not the same music, but it's totally an allusion to Broadway Baby.