@reloaded How big of a company do you want to be running? Are your dreams Fortune 500, a state-wide company with 1,000 employees, or a mom-and-pop with 15 employees during the busy part of the year? Or do you really not care? The reason I ask is because the size of your dreams affects the necessity of your current job. If you wanted to be CFO of a Fortune 500 company, from what I've gathered around here, you not only need public accounting experience – you pretty much need Big 4 auditing experience. But if you want to be part of a smaller operation, then learning the private accounting side of things will count for far more than ticking and tying for a few more years!
However, I would try to at least stick it out for a year. In a year, you can see a lot of things, learn a lot of things, make your resume look a bit better (leaving after 3 months looks highly questionable), and know for sure what you're leaving. I started my accounting career in public accounting, spent a year there. Just a couple months ago I switched to private. I love it; private is always where my dreams were. However, I think that year in public helped me a lot. Primarily because public to some extent will take anyone. I had no experience, and that wasn't a problem. Private seems to always be looking for experience. This job I have now required 1-3 years experience – I had 1 year (well, I was technically a month short of a year when I applied…), so I was able to get it…but even though my public experience didn't have much overlap into what I'm doing now, it still opened that door – without it, I wouldn't have even gotten an interview.
So, as much as you may not like it, try to stick it out a year and (assuming your experience requirement is the same as most I've seen) get the CPA letters behind your name so that you can go wherever you find a good option (instead of, for example, needing it to be in audit or under a CPA etc to complete the experience).