i'm not the biggest fan of keller, especially not of the way her character is developed in s5 with canon mckeller.
however i do very much see the potential in her for a good character. and i'm all about respecting her in fandom because the show wouldn't.
i think everything about her needs to be put in the context of her age and life experience. she went from being a kid to going college at 16 to medical school to the sgc right to atlantis and is then thrown into a command position against her will. at what? age 25? 26?
her big flaw throughout the show is that she is insecure. she doesn't believe in herself the way the other characters in the show do, although she is almost always proven to be capable and correct. (this makes a ton of sense when given the context of her life)
she's an interesting foil to rodney in this way. both kid geniuses. both complaining when put into uncomfortable situations. the difference there being that rodney complains about the *situation* not his ability to handle it, whereas jennifer complains about her ability rather than the situation. however. much like rodney, jennifer also always gets shit done despite complaining the whole time. and she doesn't quit the expedition, despite having every reason to early on.
my favorite jennifer episode is actually s5 e17 infection. here she is seen to be extremely competent, but again insecure. she tells rodney she's not comfortable making galaxy-changing decisions, but she's doing her best (rodney's offhand response being, i think, the biggest point against the two of them as a couple). she also shows how much she knows about and cares about the team and the expedition's mission and the pegasus galaxy at large.
another great episode for jennifer is s4 e13 quarantine. once i get over my frustration that there's no follow through on ronon's relationship with jennifer and actually focus on her actual characterization within the episode, i'm always amazed how much i like her. she's so young and she is so capable and she wants to do her best so badly. she's sweet and funny and awkward and. really. she just needs, as most people do, people and community to boost her confidence.
also. she genuinely cares about rodney (and his relationships with his team!). i think this often gets muddled with the shrine business, but it doesn't come out of no where! multiple times in the second half of season 4 and early season 5, she's very gently smitten with rodney, for because she thinks he's funny and kind to his friends, which she likes!
so. jennifer. she's a very competent doctor, both in research/theoretical and in direct practice. she cares about doing her work well and she worries about letting people down. she's young and surrounded by people who are confident to the point of arrogance and who all have at least a decade on her in experience (in the field, if not in life in general). she likes all of them and wants to live up to their example. and she's doing her best to get there!
it can be very difficult to find fic that are gentle with jennifer. frustratingly (because of the misogyny) i think the easiest "in" for jennifer fic is jennifer/rodney/john fic (also this tag combo). there are sooooo many good ones.
there are also many authors out there trying to treat jennifer with respect when breaking up canon mckeller post-series. i think this is more common now than in earlier fic, BUT there are certainly many wonderful fic written about jennifer across the decades of this fandom <3 (here's the works tagged with keller in my own bookmarks. i can't guarantee that they're all kind to keller, but how an author treats jennifer is something that's often on my mind while reading <3)