Is this fallacy of composition and division in the same argument?

Here is an anti vaccine meme that I ran across today on FB. 

"Ive got a question. If I didn't get the first three jabs and go straight to the fought one, will that one work? Or do I need to take the first three jabs that don't work in order to make the fought one work? Laughing emoji three times!" 

Aside from some unsupported claims (e.g., the first 3 vaccinations "didn't work") it sounds very much like an old-timer I used to work with while I was much younger waaaaay back in the last millennium.  When we finished a task (like loading or unloading a pile of wood, or moving bails of hay, or ...), he would sigh and say, "I sure wish we had found this last stick or bail when we started.  If we had taken this one off first, we would have been done a long time ago."

The claim in Jason's post works better (but not necessarily all that well) as a bit of comedy than it does as a logical argument about vaccinations.

There's no argument, it's just a misinformed meme. The previous jabs  did  work (in that they reduced rates of transmission and serious illness).