You have some great advice here about getting to know the breed, making sure your kids can be around one without having symptoms, being able to get along with the breed and esp taking the food away. We did that with our dog (a setter), it's an effective way to let the dog know who is the "alpha" dog - you.
Are your boys allergic or just have asthma? I ask, because my son and I have asthma and we have a house full of pets, they are not his triggers. His triggers are the same as mine (I'm so sorry to have passed them onto him) being sick, seasonal allergies and temperature changes. We even had him tested, he is not allergic. The animals do not hang out in his room (well, the frogs and lizards do) so he does not have the fur/dust accumalation where he spends 11 hours a night sleeping. He also does not have a rug in his room which greatly reduced his asthma attacks.
My kids were 18 mo, 7 and 8 when we got our dog. We brought our older kids with us to "puppy school" which helped them learn to interact properly with the dog. It also taught them what not to do, like feed her their snacks, pull on tail, etc. They are good about paying attention to her, letting her in and out if needed. My kids are able to feed her if we remind them and they pick up dog poop in the yard. They aren't able to walk her because as a setter she is too strong for them, even though she is well behaved she just has alot of energy.
We have an electric fence which is wonderful, the premise is not really the shock, but the beeping of the collar before they get to the shock. The only time we have a problem is when the battery in the collar dies. It gives her much freedom in the yard, but safety as well.
Overall dogs are almost as much a commitment as a child, but I think all our animals enrich our lives (we have cat, dog, bird, frog, lizard) and teach kids important lessons about caring for all God's creatures.