Yes, they will shift south.
When you observe the night sky from a location further south, you will see different constellations that are not visible from a location further north. The stars and constellations appear to shift position in the sky due to the observer's change in latitude. Therefore, as you move south, constellations that are normally visible from 34˚ N latitude will appear lower in the sky or may become invisible, while new constellations that are only visible from southern latitudes will appear.