You can always work up to it. I started out barely plodding along at 2.5 mph walking and now I run 7.5 - 8 miles a day on a 3 days running 1 day resting schedule. Used to be a 6 days running 1 resting schedule but I just can't sustain it anymore with a calorie deficit at the same time and the speeds climbing ever higher.
Do you have a treadmill? That's a very convenient place to start especially for someone with the demands of a child, since you don't even have to leave your house. You can run in your underwear at 5 in the morning when it's pouring rain outside and be perfectly comfortable and no one is going to even make fun of you for how you're dressed(except perhaps your husband in your case).
Granted a treadmill is a major purchase, I have one and I will never go back to not owning one again in my life, so useful. If you consider one though take my advice and get a good one. I bought a cheap one, and basically killed it with use. Fortunately for me I managed to get it rebuilt under warranty. If I had to do it again I would go for a sole treadmill exclusively, great price for performance, but it is definitely a big investment. About $1400 minimum if you are in the U.S. for a sole.
Your doctor is the best person to ask first, and a training program like that one is fine I am sure, though I would be inclined to just wing it like I did and feel it out for myself running and progressively upping my impact. Granted a treadmill also makes that much easier because you can micromanage impact.
A good heart rate monitor wouldn't hurt that will help let you know if you are overdoing it. Learn your appropriate target heart rate and try to stay in a safe and optimum range while running.