This quest does not show up on your quest log until finished.
Talk to Nenne, who can be found in the third house in Watchdog Alley. After talking with her, you will now have access to page 3 of the diary.
Page 3 may not be viewed while the quest The Medicine Woman is active, but will show up immediately after completion.
Go to the top floor of the first house in Watchdog Alley (G-7), there is a diary. You must read one page in order for the next one to show up, so you have to read the pages in order. If you do not get the option to read all three pages, you may not have enough fame. Page 3 tells you what item is needed to cure a cough.
Speak with Amaura in the second house in Watchdog Alley. She asks you to bring her some Thyme Moss.
Thyme Moss can be found by clicking on the ??? at (F-9) in Davoi, the Orcish stronghold. To get there you must enter the river at (H-8) or (J-10) (the J-10 route is probably safer as it allows you to bypass the high-level mobs in the central part of Davoi) and travel west through the river to get to the land at (D-8). Next go east all the way till you find a plank of wood. Under the plank is the ???.