A journal written by frontier settlers will most likely not mention Manifest Destiny much. This was an idea that permeated policy, but it was rarely openly stated, especially among common people. However, the journal is likely to mention some ideas related to Manifest Destiny, such as the superiority of Western culture.
A journal of this type is also likely to mention how life was at the "frontier" and how American Indians struggled to keep their lands. It would also outline the difficult situations that settlers faced, such as being alone, being exhausted and being attacked by Native Americans.