Short answer: yes. Practical answer: depends. Let's assume your girl is in Rio.
Most of the problem part is -- Oregon is UTC -8 (PST) and Rio de Janiero is UTC -2.
for January 2 2013:
Sunset is 19:42 her local time, 13:42 your local time. So she has to wait until sunset for you. Which is 01:42 the "next" day for her time.
Absent her being being asleep and lunar position where the moon does not cooperate, being apart does not preclude you two seeing the moon at night at the same time. The only other factor is clouds - Oregon is IMO eternally cloudy this time of year.
I don't know about Rio.