A United German Empire by Frederick the Great is difficult, and even then I really doubt it would end up in a situation where the Kaiser had much power. If anything, I figure the Hohenzollern Kaiser would be little different to the previous Holy Roman Emperors in regards to actual power. I sort of imagine the POD would be during the Thirty Years War or before that. Protestant North Germany breaks free from the Catholic, Hasburg Emperors. They first establish one of their own, who also aren't powerful enough to try and overpower the other German rulers (thus, the Hohenzollerns-who also happen to ), as a counter-Protestant-Emperor. Obviously this doesn't work in establishing an internationally recognized Protestant Holy Roman Emperor. So they convert this anti-Emperor as a Kaiser of a new, North German Confederacy State. In this altered 30YW, Denmark and Sweden prefer having this buffer state that is too internally disunited to threaten them but still there to draw any Catholic aggression, and so they recognize it.
You could by the time of Frederick the Great end up with a revanchist Hasburg Emperors, that had since this split focused on Italy and the Ottomans, aiming to reestablish their control over northern Germany. So Frederick the Great is trying to prevent this, while also turn his ceremonial power into actual power through military victories. I'd imagine a French-English switch during the 7YW, with France supporting North Germany to keep the Holy Roman Empire divided and England seeking to recreate a land threat to France to force France to devote more strength to its army and away from its army. Although maybe England just sits this one out. North Germany wins, Europe is still divided. Habsurgs win, France has the Holy Roman Empire back in its flank. Not sure how having a Northern German Empire to its south would affect Scandinavian history without really stretching.
Assuming Frederick still wins, it probably crushes all Hasburg hopes of retaking northern Germany to the Holy Roman Empire. so they probably focus more on Italy and the Balkans. The latter really changes things with the Ottomans, and could bring about earlier tensions between the Hasburgs and Russians. This Northern Germany probably wouldn't include Bavaria or the other Catholic German states, so it wouldn't end up as powerful as the OTL German Empire even if it lasted to the 20th century.