All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The reality of Istikhaarah prayer is to put the matter in Allaah's Hands and let Him choose for the person [who seeks His Guidance in a given matter] what is best for him, and then enables him and facilitates the means for him to achieve it. So whenever a Muslim wants to perform any act, it is permissible for him to perform the Istikhaarah prayer and then act accordingly. If there is any good in that matter, Allaah will help him and make things easy for him to achieve it, but if there in no good in it, Allaah will drive him away from it.
Since the matter with this girl is still at the engagement stage and it appears that it is difficult for both of you to reside in one country, then we consider that it is more appropriate to nullify the engagement as the latter is just a promise and it is permissible for both parties to invalidate it whenever they wish. When there is a sound reason to invalidate the engagement as it is the case here, then this is more evident. It might be that nullifying this engagement is something good for you and for her: Allaah will bless you with a righteous wife other than her, and bless her with a righteous husband other than you.
Allaah Knows best.