This is not a new idea it an old one, with some revisions made, that I am currently reconsidering (file says last modified April 09, 2004). This is from before Inuyasha was finished so I had not watched the entire anime or read the entire Inuyasha manga (still haven't gotten around to doing that).
On one of Kagome's forays into the past she is injured by a youkai requiring medical attention beyond the abilities of the healers in the feudal era. Inuyasha brings her through the well to her family and they get her to a hospital where the doctors do manage to save her life but it will be some time before she is fully healed. The hospital is short staffed, so Ranma and Akane volunteered to help when asked (Akane primarily transporting various items from unit to unit and visiting patients keeping them company, Ranma having some preexisting medical skills is working as a volunteer medical orderly/nurses assistant doing things like feeding patients who can't feed themselves, transporting patients, and helping nurses move people that are too heavy for them to move themselves). One of the patients Akane visits is Kagome and Kagome opens up to Akane not expecting her to believe her. Akane, of course, does believe her having seen things that are as strange or even stranger than what Kagome tells her. Akane and Kagome become friends and Kagome asks Akane to bring her somethings from her house (she did not think of asking her family members when they had been there).
Akane goes to the shrine that Kagome lives at and is attacked by a yōkai Naraku sent through the well (an ability Naraku only recently acquired). Akane puts up a good fight but the yōkai is simply too powerful and it takes the unconscious Akane through the well thinking that she is Kagome. Back in the feudal period Inuyasha intercepts the yōkai when it exits the well and kills it after a brief but surprisingly difficult battle. Inuyasha has no idea who Akane is but can smell Kagome on her. Inuyasha brings her to Kaede.
At this point I was conflicted as to what I wanted to happen. Should Akane stay in the feudal period for little while and Ranma tracks her down following her to there? Should Inuyasha bring Akane back through the well and Ranma mistakes Inuyasha for someone trying to kidnap Akane? Should Akane come back and explain to Ranma what happened and both of them go back to help Kagome and Inuyasha?
That is all I had for this idea at the time, though there were additional notes comparing Ranma to Inuyasha and speculation for how they would interact.
A story in which Ranma just joins the Inuyasha gang in their fight versus Naruku may interest some, while I do not remember where I was originally going with this fic idea, I don't really see the point in doing that. Sure Ranma would help, particularly if asked, and I could have Ranma try to play match maker for Inuyasha and Kagome or Sango and Miroku (Ranma does attempt to hook people up in the manga). I think I'd rather have Ranma find something out while in the feudal period that leads to him making changes in his life and alters his view on a few people. Ranma then going off on his own, or maybe with Akane or his other fiancees possibly Kodachi since those fics are rare, to deal with a different problem that he stumbles upon while the Inuyasha gang continue to deal with Naruku.