Perfectly fine to take him outside. Only issue is making sure he doesn't get over heated, which is more of an issue when they're older and working up a sweat outside. <img src="i/expressions/face-icon-small-smile.gif" border="0">
As for the dog, unless he's allergic, shouldn't be a problem either.
Being that it's a grandchild and the parents may be a tad overwhelmed with everything regarding the diagnosis though, you may want to follow their lead. If they have issues with the dog, you may just want to keep it in another room for now.