do you believe I could reapply in such a short time or leave it for the future and get some more experience?
Sure, you can reapply. The more interesting question would be, does it make sense to reapply? I think that's what you were getting at here:
It looks bad and they might think I mock them? But on the other hand I learn and get experience (not work experience) and it might look positive
It's hard to answer that question without knowing more specifics, so instead of a specific yes or no answer, I think it makes sense to give you some guidelines.
You need to base your reapplication timing on a reasonable time frame to acquire the skills you were missing the first time you applied.
You mentioned that you have gotten more experience since the last time you applied, but we don't know if that experience fills the gap the employer was seeing in you. If they gave you specific feedback, you should reapply once you've closed that gap. For instance, if they were looking for someone with a specific certification that takes a month to achieve, and you've spent the last month getting it, then yes - reapply.
However, if they were looking for something more long-term, like 3+ years experience doing X or Masters degree in X or equivalent work experience and you haven't achieved that - since it seems clear you couldn't have, given that those accomplishments take years and you're indicating it's only been a few months - then no, don't reapply.
If it wasn't clear to you what the specific gap was that caused them to reject you the first time, then it makes sense to reach out to them and ask for clarification. It's a reasonable question, it will show you're interested in not only the job but also in improving yourself, and it'll give you a specific goal to work towards.
In summary: It's not so much about how much time has passed, it's more about how much you've achieved in that time and whether or not it closes the gaps you had the first time.
