Our 9 months old has eczema too. We haven't kept him from our dog or kept our dog from furniture (incl our bed and sofa). We put on the epimax cream daily for our baby and his eczema seems to be much better nowadays. The pet hair hasn't made it worse, for us at least! 🙏🙏
It can do, but equally, eczema can also have nothing to do with pet hair. I've had eczema since I was a baby and even through periods of not having pets it has been bad enough to need steroid creams. I'd just keep using some gentle moisurisers like e45 cream (has worked wonders for my little boy so far) and see if that helps it to clear up, if it does then it should be easily manageable and you won't need to worry about pushing away your fur baby, if it doesn't help then you could try keeping the dog away for just a few days and see if that makes any difference x