How often do good journals publish amusing little corollaries?
If other people share your enthusiasm for the observation and the proof, then it's of interest to journals. I would just contact one of the editors and see what they suggest. It's their job to be in charge of these questions.
It is hard to know what you mean by "amusing" without seeing the paper. If you mean it literally -- i.e., the main purpose of the result is to entertain the reader -- then a strong research journal will probably not want to publish the result, as they are not in the entertainment business. A journal that publishes many short amusing pieces is The American Mathematical Monthly -- which is not to be scoffed at, as it has one of the highest readerships of any mathematical journal. However, this journal is for papers that are readable by a quite broad mathematical audience (although, to be fair, the breadth of the target audience varies quite a bit from article to article). If it is closely related to a major recent theorem in your subfield, it may be too specialized for the Monthly.
But let me take a step back and address the question of publishing a very short paper. It is my understanding that many journals are quite happy to do this. I don't know any journal that would reject out of hand a very short paper (with obvious exceptions like Transactions of the AMS, which is the AMS publication for papers too long for the Proceedings of the AMS), but there are some strong journals that specialize in short papers -- e.g. Mathematics Research Letters -- or very short papers: Comptes Rendus has a six page limit.
My impression (though I am not a journal editor) is that editors like short papers just fine. On the other hand, it is demonstrably true that the average length of math papers has increased over the years, though there is also variation from subfield to subfield (my impression is that e.g. in some parts of combinatorics it is common to write many short papers). I just looked back at my own work, and I have one three page note (published in the Monthly) and everything else is at least six pages. This despite the fact that I often started with a manuscript that was four pages or less. I think it is as you say: if you have something, it is natural to build on it. In most branches of mathematics it would look much more reasonable to publish one 30 page paper on a subject than a length ten sequence of three page papers on the subject. So if you end up with a three page paper, then it is likely that it does something quite remarkable or it cannot be evidently expanded into something more.
(Or maybe not. I am currently editing a paper written with my PhD student. At the moment it looks like the final product will be about three pages. In this case the result that we get is more than amusing and less than remarkable, but pushing it further is meant to be part of my student's thesis work rather than a collaboration between us.)
Anyway, one of the benefits of a short paper is that...well, it's short. So I would say that you don't have to figure it all out in advance. How long should a referee spend on a 1.5 page paper with a statement that's easy to understand and a two paragraph proof? Adding four more months, you can be reasonably confident of receiving a report in roughly four months, shorter if you're fortunate (and, sadly, longer if you're unfortunate). So submit it somewhere and see what happens. You may as well try a very good journal first -- really good math journals have made a point of getting "preliminary reports" and (often) quickly bouncing back papers that are not up to snuff.
It can't hurt to write it up. Even if your first journal of choice doesn't accept it (due to their editorial policies) some other journal will (if it is indeed as interesting as you think it is). Also, some journals publish brief "notes" in addition to full-fledged articles. Look at recent issues of specific journals in your field to see if they have something along those lines. Do they contain brief papers which feature proofs of interesting but not ground-breaking results? If so -- send your paper there. If not -- send it somewhere else.