How Fit Are You?

Just lately I've been giving some thought to how fit I am. I think I'm pretty healthy and thought I was fit because I walk the dogs for over an hour at least 5 days a week, surely I must be fit doing that. But what does being fit mean? Is it about being able to climb the stairs without getting out of breath, going away for a weekend of hill walking, or an afternoon playing with the grandchildren in the park? It means different things to different people. According to a Google search being fit means: "Maintaining a healthy weight with diet and exercise relative to the amount of muscle, fat, bone, and other vital parts of the body, and being able to fulfil your daily needs and requirements without pain or stress". My weight and diet are usually good, with the occasional lapses, but the reason I've started thinking about fitness is because of something that happened about a week ago whilst walking the dogs. 
We were doing one of our usual routes alongside a field. The crop has been harvested and the field is now bare so you can see way over the other side of it, and way over there was a rabbit. Buster took off first swiftly followed by Rufus. There was no way I was going to get them back, they were focused on the chase. I knew they would give up and come back soon but my worry was that this particular field runs alongside a road and if the rabbit headed that way and ran into the road R & B would follow, they have no road sense. I started running, well a bit of fast walking and a bit of running, to cut a corner and try to get ahead of them. After a couple of minutes I saw them coming towards me, I was so relieved to see them and to stop running as I was very out of puff, my heart was going like the clappers. 
So the conclusion to this is that yes I'm fit enough to walk 1.5 miles a day but the pace of my walking doesn't exert my heart therefore do I need to start upping my activity? I've always been fit and enjoyed physical activities. I was a very good athlete at school and loved PE. In my 20's I went to exercise classes, and then gyms, did a bit of jogging, cycling and swimming, walks with the ramblers and hill walking, but dog walking is my only exercise now.  I would quite like to join a gym, but unless one opens next door to where I live I know I won't make the effort to drive there. I would like to start cycling again but the traffic on both country and main roads scares me. So ...... I have a few alternative options - I could start jogging around the village; I could go back to swimming; I could join a gentle keep fit class ......... but as a starter I am now walking at a faster pace, it isn't a route march but I can feel my heart rate working. I want to enjoy a good state of fitness for as long as possible.