In the Voyager episode "Resolutions" Janeway fairly quickly is setting up traps to find the insect that transmitted the virus to her and Chakotay. At the same time Janeway is also trying to befriend a primate that might have built up anti-bodies to combat the virus. Chakotay states in the episode that he had detected primates on the planet. Why didn't the doctor think to find the insects and/or transport a primate up to sick bay so he could analyze it's blood for anti-bodies?
Who says the Doctor didn't? The Doctor had Janeway in stasis for 17 days, and studying the infection vector and local primates who may be immune would be a standard part of the Doctor's research into a cure.
Janeway likely collected more insects because she was out of test subjects or because she wanted to try a different form of examination, not because the Doctor hadn't tried it already. Even if she didn't have any different ideas, repeating experiments the Doctor had already done would give her firsthand experience with them, which is invaluable when researching an unknown phenomenon - first reproduce what others have done, then try new things.
Janeway was setting up for a long-term study, and trying to do things in the right way. She was being meticulous and thorough.
At the time on the timeline of Star Trek Voyager, The Doctor does not have the capacity to actually anywhere out side of where holo-projectors are installed. At this point he has not recieved the device known as a mobile emitter, which alows The Doctor to travel anywhere outside of his restrictive holo-projectors.
It should also be known that like the crew does to him all the time(out of comic relief i cannot say) this question is asked a lot about missing a task. As Doctor like to point out, his sub routines will not allow him to over look even the simplist of task, as you can imagine this said task would have been already completed if the doctor had the ability to leave the ship in thr first place.
Also if this virus had infected the two members of the ship, and the insects have the anti bodies, that would also mean the virus would be in the vlood as well. Quaruntine is huge factor at this point.