Should we make our dog an outdoor dog or find a good home for her?

We recently took our 16 mos old daughter to an allergist for a skin test. She's been having bad eczema type outbreaks and they've been getting worse. Well, it turns out she's highly allergic to dog dander. We have a black lab and they just adore each other. Our dog has been with us since we found her on the side of the road when she was 12 weeks old (she's 6 now). We just paid $1500 for surgery to have a cancer m removed from her leg to boot. The allergist suggests we get rid of the dog...he said we can put her outdoors but it will only clear up my daughter's problems by 80%. I know my daughter's health outranks my dogs but I have been getting so much information and stories from people in the same or similar scenario where they kept their dogs and made things work out and then I heard stories about how people got rid of theirs and then when the kid was like 16 they introduced a dog and things were fine. It's such a tough decision that I thought I'd never have to make.