Thanks for the info. mnemosyne. Alas, my lease says ‘no pets’.
From here: http://www.ltb.gov.on.ca/en/Key_Information/STEL02_111463.html
Your choice about whether you want to risk the wrath of your landlord, but you cannot be evicted for getting a pet. Or you could move 
My friend’s dog was snapping at imaginary insects in the air last night, so cats most certainly do not have a monopoly on weirdness.