What is MHT district office?
Other good solution would be to wait and apply in mid June, so hopefully nothing will happen before you return from your trip. N-600 only has one possible step (and it doesn't always happen). The only possible step is that you get called for a formality interview with you and your child, and if that happens I think they give you the certificate on the spot, so it happens at the end of the process, not in the middle. I think N-600 in most places take about 6 months, so I think you should be fine even if you apply now.
DO : San Jose
11/28/2006 : Mailed
12/04/2006 : PD (and Receive Date)
12/05/2006 : Check cashed
12/11/2006 : Notice Date (Received on the 14th)
12/22/2006 : FP ND
01/09/2007 : FP Appt
12/29/2006 : FP Done. Walk-In
07/17/2007 : Interview (ND May 17)
08/22/2007 : Oath (Received Jul 26, issued on the 23d, mailed on 24th)
08/23/2007 : Applied N-600 and Expedited Passport
09/06/2007 : Passport received
08/20/2008 : Sent N-565 (Approved Feb 17, 2009)