I don't recall SQR having the ability to schedule a process request built in; PeopleBooks mentions that outside systems could use the component interface to schedule a request, however, I have not done that with SQR before so I'm not sure if/how that's feasible.
I would take the approach of running a job instead of your original SQR. The new job would include your original SQR followed by an App Engine process that schedules the needed SQR process instance on the date you need.
Without knowing more specific details about your process, here's a code snippet of what you could run within the AE:
Local ProcessRequest &processRequest;
/* Create the ProcessRequest Object */
&processRequest = CreateProcessRequest();
/* Set all the Required Properties */
&processRequest.RunControlID = "YOUR_RUN_CNTL_ID";
&processRequest.ProcessType = "SQR";
&processRequest.ProcessName = "YOUR_SQR_PROCESS_NAME";
/* Set any Optional Properties for this Process */
&processRequest.RunLocation = "YOUR_PROC_SCHED_SERVER_NAME";
/* You would set the run date time to your future date */
&processRequest.RunDateTime = %Datetime;
&processRequest.TimeZone = %ServerTimeZone;
/* Schedule the Process */
&processRequest.Schedule();