Should we pray for
the peace of Jerusalem?

Yes, you should, but only the Jerusalem that God cares about. He does not care for the Jerusalem in the Middle East, because He rejected that city nearly 2000 years ago. While David wrote Psalm 122 regarding the stronghold of Zion that was the capital city of O.T. Israel, his words today can only be applied to the church and kingdom of Jesus Christ, for the only Jerusalem that matters is the one above (Gal 4:21-31; Heb 11:9-10; 12:22-24; 13:14; Rev 3:12;21:2). Jesus declared that earthly Jerusalem would be trodden down of Gentiles until this age ends (Luke 21:24).

See Also

True seed of Abraham and its consequences: Seed of Abraham.
Rebuilding of David’s kingdom with Gentiles … Dispensationalism’s Best Verse.