If you are just starting out to study Japanese, it will be a miraculous feat to pass 1-kyu. I don't think there is any restriction against people taking it, but you have to be some sort of wizard or have tons of time on your hands to pass within a year through self-study.
USD1500 amounts to about 178,000 yen at today's exchange rate. Bare subsistence wages, but I don't know what dormitories ask, or if you plan to stay in your own apartment. Go the latter route, and you may have to pay 5 times that amount just to move into a bare apartment (that means nothing there, from appliances to light fixtures). You're going to need pretty high level Japanese to attend those schools, too, but I think you already realize that and may just be planning ahead. If so, I'd say plan further ahead.