Sorry, but no. Personally I don't think you are. I would have loved to have my own horse after 4 months of riding, but the horses I was riding then is much different than the horse I ride now. Buying a horse is a huge purchase, so you want to make sure you're buying a horse that'll last you a few years. I've been riding for 10 years and I can honestly say that I would not want to own any of the horses that I rode in my first year of riding. They weren't bad horses or anything, but they were suited for beginner riders, not people who do 2'9" hunter/jumper courses (which is what I do now). Basically, if I'd bought a horse then I wouldn't be able to move up with it. Since you say you're a quick learner, I'm guessing you probably don't want to be stuck with a beginner's horse for a long time.
I think you need to spend a few more years learning how to ride, but also learning as much as you can about taking care of horses. It's a big responsibility, so you want to make sure it's really what you want.
What if you decide owning a horse or even riding in general isn't for you? People think it won't happen, but it still does. And imo, I don't think that's something you can determine with only four months of experience. If you can find an opportunity to full lease, I would recommend that. Most full leases don't require sharing a horse, and it's pretty much just one step below owning a horse. Sorry I kinda went off on a tangent in that first paragraph, but I'm hoping my point got across regardless.