Should I consider getting a cat even if my girlfriend isn't in favor?

I'm a 22-year-old male, and I've been in a wonderful relationship with my girlfriend (21) for the past year and a half. She is an amazing partner—loving, kind, and generally a great person. I care for her deeply. While we don't live together at the moment and have no plans to for a while, she is currently in graduate school, and I've just finished college and started working full-time. A bit of background: I've always had a passion for animals and have dreamed of having a cat ever since I could remember. Now that I have my own place post-college, I'm really looking forward to getting one. My girlfriend also loves animals, but she prefers not to keep them indoors. Early in our relationship, she made it clear that if we were to marry, she wouldn't want pets living in the house. I mostly agree with her—I'm a strong proponent of outdoor dogs—but I believe that cats can thrive indoors if cared for properly, as they are generally clean animals. We definitely differ on this opinion. Now I'm torn about whether to get a cat. I've been bringing it up frequently because I'm really excited, but I can sense that she doesn't share that enthusiasm. Whenever I mention it, her mood shifts and she seems a bit down. She's never outright told me not to get a cat, as she would never do that, but she has expressed concerns about feeling uncomfortable around cat hair. I've reassured her that I would keep my apartment clean to ensure she wouldn't notice any mess when she visits. Part of me wants to adopt a cat just to demonstrate that it’s possible to maintain a tidy home with a pet. However, I don’t want to jeopardize our relationship by bringing in a cat, but I really hope to have one. What should I do? Oh, and I should mention that I live in a one-bedroom apartment without a yard, so the cat would need to stay indoors.