With all due respect, you are wasting your time. This weight you are gaining is not the kind of weight you want to gain. As long as you do not train and you do not follow a strict muscle gaining diet all you earn is fat. It may not be visible (subcutaneous fat), but it is still there and this kind of fat is even more dangerous (visceral fat).
Don't leave for later what you can do now. Start training as soon as you can and don't be discouraged if you don't see any visible results immediately. I've been like you, about 55kg 4 years ago and now I am 75kg.
You can achieve your goal by following a training schedule that is aims for muscle mass. The training routine is different for each body section, but all follow the same rule, High Intensity - Heavy Load. In fact there is also a debate regarding which is better here, but I like to combine them.
TIP: Life has taught me and later I was told by a physician as well, that the number one reason one does not manage to gain muscle mass is the fact that they do not train their legs enough, so be sure to train your legs enough when you actually start.
One last thing: I believe it is of vital importance that you know and fully comprehend the significance of avoiding overtraining and its ramifications so when you have time read this article.