This herbicide is used extensively here in the western U.S., and considered, generally, safe. However, it is recommended that non-grazing animals be kept out of the area receiving the application until thorughly dried as derry advises. Depending on weather conditions this can be 24 to 48 hours.
Although Roundup kills plants by blocking an amino acid synthesis pathway found only in plants not mammals, it's still recommended that grazing animals not be allowed back into the area for 10 days to 2 weeks.
There are unconfirmed, anecdotal reports of deaths of animals due to exosure, but the overall results have been satisfactorily safe...