You count the 30 days from when your notice is given, and it doesn't have to be given on the 1st of the month. Once given, it's up to the landlord if she will rescind it. If you are already in the apartment, I would think she would be happy to extend the lease if you asked to withdraw the 30 day notice. You can always tell her that you'll agree to another year lease. If she has the assurance that you're committing for a longer period, then it is more encouragement for her to keep you. If you vacate she will have to clean, advertise, and the transition won't be from one day to the next. You are a known quantity to her.
Scott Rights, Esq.
Normally, you cannot rescind a 30 day notice to terminate. However, if your landlord is willing to give you an extension of time to move out, it is fine.
Practically speaking, if you fail to move out by the 30th day, the landlord must file an unlawful detainer lawsuit against you. The eviction process could take at least 30 days.
The information presented here is general in nature and is not intended, nor should be construed, as legal advice. This posting does not create any attorney-client relationship with the author (who is only admitted to practice law in the State of California). For specific advice about your particular situation, consult your own attorney.