I think you could easily do it.
Just as an example there is this training program http://www.halhigdon.com/halfmarathon/novice.htm that takes people from running less than you are now to a half marathon in 3 months. I'm not saying you would want to use this program exactly (you'd almost certainly want to do more cross training than is there) but it does show that you have heaps of time to build up