If there was a universe with the same laws as this one, but there were only bosons in it, would QM 'do anything'?
Would there be any QM effects - such as an energy level (but that would require fermions..).
The existence of "bosons" is already a consequence of QM -- the notion of indistinguishable particles and the resulting Bose-Einstein (as opposed to Maxwell-Boltzmann) statistics is manifestly not a classical phenomena. Classical particles are always distinguishable, since "that particle there" has a complete set of observables that classically commute with each other and with those describing "this particle here".
WSC - Not all matter is made of fermions. Things such as helium-4 and carbon-12 are bosons, and there are are many other composite particles and molecules that are actually composite bosons. Any composite particle with an even number of fermions, and thus with an integer value of spin, is boronic, which to me seems a little moronic.
I imagine that you are thinking primarily of the force carrying bosons and not the many composite bosons. It is easy to loose track of which particles are in which family as there are so many ways to classify any particular compound. I think that there is something wrong with a classification system that groups the magical force carryi Png particles with something as interesting as, but as entirely different (to me at least) as helium-4. Yes, helium-4, especially when ultracold and behaviour as a superduper fluid, is wonderful, but it seems like it should be in a different family than the Higgs boson, photon, as well as the weak and strong force particles and the colorful gluon zoo. Perhaps composite bosons should be called something else. I propose "PartyOns"