This can be accomplished with content rules to inject the query string into the redirect path.
Create a 'Content Matching' rule and a 'Replace Header' rule.
On the left hand side of the WUI, click Rules & Checking > Content Rules > Create New.
|Value of Header Field to be replaced||\1example.com?\3|
Create a SubVS and enable 'Content Switching'.
Assign the content matching rule (match_query), to the SubVS.
Within the parent Virtual Service, assign the keep_query rule under Advanced Properties > HTTP Header Modifications > Response Rules.
The final step is done within the SubVS in Advanced Properties > Not Available Redirection Handling. You can either set a 301 or a 302 with http://%h%s in the Redirect URL.
It is important to note, that the SubVS must not contain any Real Servers.
Also, this example outlines a port 80 unencrypted Virtual Service. The same concept applies for a port 443 service, however you must enable SSL Acceleration at the parent Virtual Service. The LoadMaster must be able to decrypt traffic.
In these examples, the following requests:
> GET /?kemp=loadmaster&support=true HTTP/1.1
> GET /query?kemp=loadmaster&support=true HTTP/1.1
> GET /query/test?kemp=loadmaster&support=true HTTP/1.1
> GET /query/test/balance.php?kemp=loadmaster&support=true HTTP/1.1
> Host: example.com
Will all return this 302:
< HTTP/1.1 302 Found
< Location: http://example.com?kemp=loadmaster&support=true