In Ender's Game, who fired the Little Doctor?

An unnamed pilot of a ship in Bean's squadron

In Ender's Shadow we get the final battle from the point of view of Bean, and there is some additional info given as to which ships actually fired it, with the implication being that it was a pilot in Bean's squadron.

The enemy understood now, and rushed to destroy the plummeting humans. Fighter after fighter was picked off by the inrushing ships of the Formic fleet. Only a few human fighters survived long enough to enter the atmosphere.

Hold on, thought Bean. Hold on as long as you can.

The ships that launched too early watched their Dr. Device burn up in the atmosphere before it could go off. A few other ships burned up themselves without launching.

Two ships were left. One was in Bean's squadron.

"Don't launch it," said Bean into his microphone, head down. "Set it off inside your ship. God be with you."

Bean had no way of knowing whether it was his ship or the other that did it. He only knew that both ships disappeared from the display without launching. And then the surface of the planet started to bubble. Suddenly a vast eruption licked outward toward the last of the human fighters, Petra's ships, on which there might or might not still be men alive to see death coming at them. To see their victory approach

_{Ender's Shadow - Chapter 23: "Ender's Game"}

The actual pilot of the ship is unnamed, but he would have been one of the ones sent out to the bugger homeworld at the end of the Second Invasion.

There is some fan speculation that it is Bingwin, an Ender-like character in the prequel books. However the prequel books still haven't reached the point where the fleet got launched.