You can quit and remain in Canada until your permit expires. However, you cannot work for another employer unless & until you obtain a new work permit.
If you have any hopes of applying for permanent residence with Canadian work experience, I would strongly recommend sticking it out for at least one full year - minimum of 52 weeks (through July 2018).
As for notice period, that should be in any kind of contract or letter of appointment. It would be a minimum of 2 weeks, but check your contract. If you want to stay on good terms with your former employer, you would need to figure out the norm for your position and company. The more senior positions usually expect more time.
