I would like to attach Constituent query to a dashboard, but it doesn't seem to be an option. Am I missing something?

Since this isn't an option, I thought I would attach a Gift Query instead, but then I soon ran into another problem, I can't figure out how to include the Alumni Education information to the output of a Gift Query.

 I would like to do the same - to see new registered users in NetCommunity.

 You can build a dashboard on a constituent query, you just need to attach it to the Solicitor Query panel type in dashboard.  That's the only one that allows for you to use a constituent query.