Not a stupid question at all. The answer is: yes. https://en.wikipedia.org/wiki/Trojan_(celestial_body)

Theories for the formation of our moon suggest a Mars-sized Trojan collided with earth before it was earth: https://en.wikipedia.org/wiki/Theia_(planet)

Langrangian points L4 and L5 are stable places where objects can orbit ahead of and behind a larger one, like a planet: https://en.wikipedia.org/wiki/Lagrangian_point

Asteroids occupying these spaces in our solar system are called Trojans: https://en.wikipedia.org/wiki/Trojan_(celestial_body)

They recently announced the first detection of an exo-moon, but said the moon was the same size as the Earth (orbiting a much larger gas planet) so the definition of planet and moon is blurry. Unfortunately the terms 'dual-planets', 'double-planets', or 'binary-planets' are not (yet) recognized by the International Astronomical Union (IAU) according to wikipedia.

Depends of your definition of planet, according to IAU a planet needs to clear his neighborhood, in this case, only one planet can be the major object in his orbit.

But co-orbital objects exist and one of the most interesting ones is the pair of Saturn satellites, Janus and Epimetheus, their orbit describe a horseshoe and there are pretty cool videos on YouTube with their orbits.

The short answer is "yes", but the longer answer is "we haven't observed this happen in practice for any significant planetoids".

There was an observation five or ten years back that originally looked like it might be two planets in the same orbit, but it turned out that one planet was in an orbit with a period exactly twice that of the interior planet.