This isn't Linus' first time with the security blanket, but it's the first time it's presented in terms of providing security. It's not called a "security blanket" yet, but it's almost there, it just needs to connect those two nouns with nothing else in-between. This is a term that entered our language largely because of Peanuts, so this is a momentous strip.
I like Lucy's loud "INSANELY happy!!" I can't picture that coming out of Nancy or Sluggo. Here Lucy is generally in favor of Linus' blanket. Her attitude later on wavers between for and against, with their blanket-hating grandmother pushing her against I think. Charlie Brown, contrary to his general opinion later, seems to be against it on principle, but willing to give it a try. Isn't a blanket more than just a swath of material, though?
Linus' expression in the first panel is interesting, an expression that doesn't read easily. The sequence from panels 6-8 are interesting for how unconcerned Charlie Brown and Lucy are about Linus' feelings throughout their conversation; his reactions to them are pretty funny.