mariloulou you sound so similar to me!! 6 wakings a night SUCKS, has it been like that every night for 5 weeks? I totally understand the feeling that you shouldn't be encouraging bad habits...I've tried putting DD down asleep as she won't go down awake or drowsy. I've tried lots of rocking, lots of co-sleeping out of desperation, loud white noise, introducing a comfort blanket, altering bed time..the list goes on and nothing has helped...but I think too many changes won't help matters and as you said I think the answer is just to ride it out and she'll sleep better when she's ready and her brain isn't so busy and wired from such leaps in her development. I'm guessing you've heard of the wonder weeks?! totally sums up DD right now who is at the peak of leap 4.
Last night was the worst nights sleep she's had ever I think. Put her down and she seemed fast asleep, went to dish up my dinner and she woke up, then again at my second attempt to eat dinner. third time worked but she only slept for 2 hours then woke half hourly/hourly for the rest of the night and was ready to get up at 5. I think I might have had 3 hours sleep max.
Oh and did I mention she was teething yesterday?! 
Naps have turned in to 30 minute crappy naps where she furiously wrestles me until she falls asleep. I've tried earlier and later wake times which makes no difference.
Poor DD had colic and has reflux, she was just getting a bit more settled before this 4 month sleep regression stomped it's way in to our lives 3 week ago! Because of this, our routine has been changed around a bit, but DD often wakes around 5.30-6am then has a nap roughly every hour and a half and feed every 4 hours, then bath, bottle and bed at around 6:30/7.
What's your routine like?