How do I query Jira to search for all issues that have been resolved within a length of time from when it was created?

You have all sorts of control with queries. For example, here is how I check for my tickets that are on hold that I have not updated in the last 5 days.

currentUser() AND status = "On Hold" AND updated <= -5d

Created in the last 5 days would be:

created >= -5d

Resolved in the last 7 days would be:

resolved >= -7d

OR

resolved >= -1w

I don't know if it matters yet but I resolved it with dateCompare():

issueFunction in dateCompare("", "created > resolved -5d"))

So since this does not seemed to be built into JIRA by default my only other suggestion is to see if you can extend JQL to add it.

How's your Java? See how to add JQL to JIRA