A laser pistol would have to have an insane amount of energy packed into a small package, which is why I say they are unrealistic weapons.
In the ED world, we have reactors small enough to fit in a Sidewinder that can power drives that warp the fabric of spacetime and open gateways into higher dimensions.
And in the real world, we have pistol sized laser hair removal devices that can actually burn your skin, that operate on a rechargeable battery.
So IMO, laser pistols powerful enough to cause fatal heat damage aren't out of the realm of possibility in the near future, let alone over 1000 years from now. But having a small-yet-powerful energy source is definitely the main bottleneck here.
Also, they would not function the way they are usually depicted science fiction. They would work more like heat rays rather than pew-pew blasters. Their payload would travel at the speed of light (Star Wars is cool and all but projectile lasers are silly) and they would be completely silent except for the sounds produced by the internal components of the device when it fires.
But you don't need to take my word on any of this, you can watch this guy's video of his HOMEMADE LASER SHOTGUN for proof of concept:
[video=youtube;iVrJUbeuG44]https://www.youtube.com/watch?v=iVrJUbeuG44[/video]