There's always the "Flair" like I have on the sidebar of my blog. Go to your profile page and look for the "flair" tab. It's not as pretty as the link/image you showed, but it shows your stats and includes a link to your profile on the site.
I'm sure that, being a PHP programmer, you already know how to use an image in a hyperlink, so I'm not even going to go there. We could probably come up with some image for our site, but I think that for the Parents.SE site, the "cutesy" image is appropriate.
I think that with the serious nature of a Christian site, the standard Flair is more appropriate and professional. Personally, I'd say we should just stick with that.