It would be nice if Notes implemented this out of the box, but since Notes is so customizable, you can build something yourself fairly easily.
Lotus Notes has a concept of a mail-in database, basically a database that can receive emails. A solution that you could implement without adding any third-party components is to create a "mail review" database to collect those group emails, then build some workflow actions allowing your moderator to approve or deny each email.
You'll need to create a mail-in database document within your Domino Directory, and configure it to go to your mail-review database. Then folks will need to send to that address and NOT the group alias. In fact, since you can't otherwise prevent folks from bypassing your system, you are better off not having the group alias at all. Instead, manage the names of that group within your mail-review database. Or at least name your group something cryptic so it is less likely to be chosen from the address book.
When emails are approved, your mail-review database will be sending them out just like you would send an email from any database. This is a key point - you're not really holding the emails for review and then sending them on their way. Emails are delivered to the mail-review database and will sit there forever until they are processed, and then you'll need to create a new email that just looks exactly like the incoming one, and send it from the mail-review database. To the end-users there's hardly a difference, but from a mail tracking perspective, they are two entirely different emails.
The only issue you might run into is controlling the "principal" or "from" item of the email. Those are automatically set by Lotus Notes based on the current id, and I'm not sure if you'll be able to completely fake out the email to make it appear as if it came from the original sender. As a workaround you could modify the subject line to include the name of the original sender, and just let the emails appear to have come from Bob (your moderator). Or you could create a special Notes user / id to work with this system and use that id for sending emails (if you put the code to send an email in a Notes Agent, you can use the "run on behalf of" property and assign that to the special user)