Can the building management charge me if I leave early?

I should've asked this earlier but I was zoned out with my work but I wonder if the building management can charge me for me leaving early.

I live in an apartment near Yonge and Bloor street and I decided kind of last minute to move out.

So according to the contract I signed when I first moved in, I was supposed to give them 60-day notice if I want to vacate my unit but I only gave them roughly 45-day notice due to this corona situation (told them I will be leaving by Oct 1 on Aug 17th). and I received the letter from the management office saying that I will be charged roughly $280 processing fee for not telling them early and I will be responsible for paying October's rent unless I find someone to take over the unit.

First of all, can they charge me that 'processing fee' for not telling them early? and can they also make me responsible for October's rent because I did not tell them that I am leaving on time? I read through the contract I signed when I moved in and it doesn't really say anything about the processing fee and me being responsible for the rent.

I don't want to pay rent for something that I will not even be living in so please help thx.