Thanks Paul. I was seeing the search result for Quick Contact module but did not realize the other was listed in the same spot for download. Further, the extension detail page should have the link corrected. This was not clear, I figured that would just take me to the download for that module, which I already have. I was trying to search "captcha" and there were no results. The image you inserted is broken for me, I am not sure what happened.
As for the option/feature being built-in, it would just be really nice to have. The idea of this module is that it is quick. I can understand in a form builder or more advanced form to have add-ons, but with the Joomla core offering the plugin it would be great to just have a setting in JA Quick Contact to toggle on usage of the system captcha.