My infant daughter(US born), has dual citizenship in Peru as well as
the United States.  She is currently living in Peru with her
Grandmother.  The Peruvian consulate here in Miami could not issue her
Peruvian Passport on time due to  Hurricane RIta.  The Immigration
officer in Peru did not stamp her U.S. Passport upon entering Peru in
August of this year, (I later mailed her Peruvian Passport which her
Grandmother has in her possesion)  Peruvian immigration officials are
now stating that she is undocumented and unable to leave the country
as they have no "proof she entered Peru".  Her Grandmother has all
documentation including both certificates of birth, both passports,
boarding pass from the airplane etc...  My question is will the
Immigration officer deny my daughter to leave Peru because she has no
stamps on either of her passports?

I believe you will find an answer to your question on 
http://es.groups.yahoo.com/group/Genealogiaperuana/
it is a private group so you will have to join. 

Once in there search for message 4839 and follow that string of messages.

Questions:

1. Where is the mother? Is she alive? Did she give permission for the
girl to come to Peru?
2. Why they didn't stamped the US passport? Who was with the girl when
she entered the country?

The Mother is alive in the US.  She gave permission for the
Grandmother to take the baby to Peru.  We don't know why the officials
didn't stamp the passport upon entering the country with her
Grandmother.

There is a procedure for extemporary stamps in passports:
http://www.digemin.gob.pe/f_pub_det_tramite.asp?cpd=364 (she has the
boarding pass and tickets as proof)
For more info, see Immigration office of Peru:
http://www.digemin.gob.pe/f_home_digemin.asp?cpd=289