If your doctor wants you to do ab strengthening exercises, then I'd ask them specifically what's safe to try and what you should avoid based on your condition. They should be able to tell you that information.
Now my doctor knows about the small hernia I have next to my belly button which I've had since my son was a baby. (He is six/nearly 7 now.) She has advised me still to do strengthening exercises to tone my muscles in my efforts to get healthier. Right now at this size, it REALLY hurts my back(feet, too, but that's not what I'm asking about) to stand for extended periods of time. What can I do to strengthen my core without doing floor crunches, which tend to exacerbate the hernia?