If you throw a peanut into the universe, will it eventually become a galaxy of it's own?

No it willl not.

No. But if you throw a peanut on the ground, a peanut plant will grow. 

There verr 2 peanuts...valking along za Strasse.

And one vuz a salted.  HEE HEE HEE   HA HA HA

Nope;  it'll remain a peanut. 

That's it's destiny. 

You don't mess with destiny. 

I am sure vegans would object to this treatment of a nut.

It's far from a certainty, but it is conceivable that its mass could increase by colliding with space  dust and other particles of intergalactic flotsam and jetsam (Earth itself is surrounded by hundreds of orbiting, discarded artificial satellites and their components). The greater its mass, the stronger its gravitational pull. Given enough time, on the order of billions of years, a planet-sized object could result. Whether it could transform into a star, I have no idea, but if so, that might lead to a planetary system if its own. But from there, a resulting star system, let alone a galaxy, seems less likely than it falling in with an existing star system. More likely is that the budding planetoid would fall into a star's gravity well, ending its epic journey to stardom.

That's nuts.         

ITS own, Eric, its own. Not it's own. "It's" is it is. No offense. Even university graduates go wrong here.

That happened once, its called the Peanut Cluster.