N600 takes a long time (6 months would be a good guess).
To get a passport when claiming naturalization through parents, you need to show
a) proof your parents naturalized
b) proof that you entered US legally on a GC ... I presume you have a GC
c) birth certificate showing relationship
d) proof that you were legally in their custody and living with them when they naturalized (school records, insurance records). Custody documents only required if there is a dispute between parents (or single/joint custody), but living with them part is required ... you should not be living in 1 continent when they are in another.
GC: EB1: 1999 ==> 2004. 3 yr delay due to lost file. N400: San Jose. Apr'09 ==> Aug'09.
I am not a lawyer, forum police, moderator, moralizer or an immigration officer. If I sound like one, use "your" best judgement.