Just wanted to join everyone else saying sure, plenty of people walk most of the races, so that's fine, but you TOTALLY have time to train to run it. I just started running in January of last year, and since then I've done a few 5ks, a couple 10ks, and a half marathon, and I'm really looking forward to enjoying running the upcoming Princess 10k at whatever pace feels good to me in the moment. When I signed up for the January half marathon in July, I had that same fear you have, and assumed I'd walk most of it. But with the right kind of training, I was able to run almost all of it. The best advice I can give you is to check in with
@DopeyBadger for help with a training plan that can get you where you want to be in a safe way, without pushing yourself too hard too fast and causing some kind of injury. I followed one of his training plans for my first 10k and another one for my first half marathon, and I'm still amazed at what I've been able to accomplish because of it. You can ABSOLUTELY do it.