Are there dextral/sinistral higher animals?
Handedness has been studied in several different species of toads. As basal tetrapods, the authors argue that these taxa are unlikely to be influenced by human hand dominance and are thus a better model for studying the evolution of handedness.

Bisazza et al. (1997) studied "pawedness" in Bufo bufo, B. viridis, and B. marinus in wild-caught animals by determining which forelimb was used to remove a piece of paper from the animals' snout or a balloon placed over its head.

The results were mixed. B. bufo preferred the right forelimb in both tests, but B. viridis and B. marinus did not. B. marinus did preferentially turn its head left in another experiment, using the right forelimb for support.

A subsequent study by Malashichev and Nikitina (2002) showed that Bombina viridis is "lefthanded," while Bombina bombina is "ambidextrous."

So based on these studies, lateralization appears to have a long evolutionary history.