There is no time too soon to start training. The fitter you are the greater your chances of summit success and the more you should enjoy your experience on the mountain. The best exercise for Kilimanjaro is to do lots of walking, preferably at an elevated pace. During work days, try to walk as much as you can ... take the stairs instead of the elevator, walk instead of driving or catching a taxi. Try to get at least an hour of walking into every day.
In addition to this, try to get some morning and evening sessions of aerobic activity in, such as cycling, running or spinning. An hour of any of these activities three or four times a week should be a great help. Weekends and days off you should try to head for the hills. Try to walk for 6 to 8 hours, perhaps even on consecutive days. Even try camping out on the nights in between, but be careful not to put yourself off the whole idea. Also, practice walking as slowly as humanly possible! One of the hardest things to deal with mentally is how painfully slow you may end up walking at the behest of the guides. This can become frustrating if you are unaware of it and the temptation to break ranks and stride out on your own will be great, and foolish.
Increase the pace, especially on uphill sections to increase your aerobic capacity. Use the boots that you will bring with you to Kilimanjaro so that they are well worn in. Lose any surplus weight, it will be much more difficult to carry around at altitude. Get as fit as you reasonably can in the time-scale available, make it a priority and make the effort. That way if you don't make it to the top at least you know you have given it a good shot.