Yes, you can take your garden sundial to the same latitude in the southern hemisphere, but the numerals would have to be reversed in a mirror-image way.
That is, for example, the displaced sundial would show 1 P.M. when it was 11 A.M.
While the sun’s apparent path across the sky moves from east to west in both hemispheres, it stays generally to the south of directly overhead above the equator and generally to the north of directly overhead below the equator.
When a sundial is used in the northern hemisphere, the raised tip of the gnomon, the wedge-shaped device that casts the shadow, points toward the north.
It is positioned to cast a shadow at the center of the dial at noon, and the hours run clockwise.
In the southern hemisphere, the tip of the gnomon would point in the opposite direction, so the hours would have to run counterclockwise.