
If you can’t bring it to school, I would wait, because a cat that young as pictured needs a lot of attention and support. However, if you have a condition like anxiety or depression, I would look into getting your health provider to write an ESA letter. I had a letter like that in college and then landlords legally cannot stop you from having the cat (and they can’t charge you pet rent!)
Assuming you live in the states, the ADA makes it so that denying you an emotional support animal (recommended by your health provider) is disability based discrimination. There’s no official “registry” for ESAs, and a letter stating that an ESA would benefit you is usually enough. Most landlords would rather let you have the cat than risk a lawsuit anyway