Satay: I did some research and found out that the one month notice before leaving has to be added to the lease length (12 months lease contract actually means 13 months, 24 months means 25 etc.) so it is not just a weird thing of my contract and in my case I just have bad timing.
I expect the landlord to stick to the conditions of the contract as she seems to be quite rigid (she did not want to pay for the painting of the apartment when we moved in etc.) but I hope I am wrong and she will be understanding.
anothercanuck: I do not have bad relationship with my landlord, I just have no relationship with her so in a city that is pro-landlord as HK is, I don't see why she would do me that favour. I will definitely talk to her but won't provide another tenant simply because nobody will accept to pay my rent for one month. We'll see...