Congrats on your progress so far! There could be a number of things going on which would cause you to feel lightheaded. How soon before the workout are you eating? If you are exercising first thing in the morning, you might try eating something small (like a banana) before you start.
Are you well-hydrated before you start, and are you drinking during and after the workout? That's especially important when it's really hot. Are you doing a good cool down after the walk is over?
"You may have a fresh start any moment you choose, for this thing that we call "failure" is not the falling down but the staying down." Mary Pickford
"No matter how slow you go, you are still lapping everybody on the couch."