And just to be a big geek I'm slightly irked straight away that there's a Benzite with a respiration device when DS9: The Ship
showed they didn't need them anymore.
Most humans don't need reading glasses anymore in the 23rd century, but Kirk is allergic to Retnax-5. Maybe something similar is the case here.
There's also a panel that describes the Doctor thus- "Emergency Medical Hologram that gained sentience during USS Voyager's long return to the Alpha Quadrant."
Hmm, would you say he gained sentience during the trip? Seems to me he grew an awful lot as an individual but was always sentient. Hard to say... what would others think?
Holodeck characters appear sentient even though they're not. One can't really tell from cursory observation just when the Doctor became sentient. I tend to think that the potential was always there, but most EMHs weren't meant to be kept in continuous use, so they weren't given the opportunity for the necessary complexity to grow in their neural networks. And the unusual challenges the EMH faced aboard Voyager
may have forced his software to drive itself to a higher level of operation in order to cope with them; and Kes's encouragement of his development probably helped as well. But I don't think a specific moment of "awakening" can be pinpointed; it was probably more a gradual emergence of complexity, like an infant growing into a child, only faster.