The light is immaterial (lol) to the holograms existence. They are only solid via fancy forcefield transmitted from the holo emitters. For all intents and purposes they seem to only exist as programs within whatever computer operates the holo emitters, whatever or whatever that may be. The only limit on where they can be is the speed of the computer system and links within it. They can send holo programs between the alpha and delta quadrants, but are limited by the speed and this can only send smaller programs. The mobile emitter often gets transported, but that's because they only have one. If the doctor is going somewhere with holo emitters they don't need to be transported and can just be data transferred.

Personal rant follows:

!The whole hologram plot in Voyager is honestly poorly thought out, and it basically feels like if you followed their logic Chat GPT would be a protected federation citizen. I get that the writers wanted to give the doctor legitimized personhood, but it feels like they forgot to think about what that would mean for literally every other hologram. !<

!Like, they give that one species holograms to hunt, does that mean they invented a species doomed to be reincarnated as prey forever? Is, Moriarty sentient, and if so is trapping him in a simulation moral? If they just run a hologram long enough does it gain sentience? How are they testing for this? Does that mean Vic Fontane is sentient even though he probably would say he isn't? What about that weird Irish bartender Janeway does - fair haven ran for a while, how long does it take? If you run a training program are you committing infanticide? Is turning off a hologram even moral?!<

There was an entire TNG episode (Season 6, Episode 12) whose plot centered around this:

Geordi and Data spent half the episode experimenting with beaming (inanimate) holographic objects off the holodeck, to no avail. With that said: