Let's say the labels are gone... Do you think that simply posting a picture of you with your child on your professional home page could also trigger warning light in the visitors? The only think I could think if is "Not again, there's too much of this on Facebook already."
Its hard to say. Some might take it as not professional. Others may not care. Some will think its cool. In my personal opinion, I wouldn't post it at all. But that's me. I mean realistically, is there a business reason to? You should ask yourself that and quantify it as such.