Nature Conservation Branch senior zoologist Sally Bryant said the pup, born on Dover Beach in Tasmania three weeks ago, has learned to swim and is accompanying its mother on fishing excursions.
Elephant seals, which normally breed on the sub-Antarctic Macquarie and Heard islands, were wiped out in Tasmania in the 19th century.
Bryant said initial worries that the mother would become anxious and abandon her pup had given way to confidence that the 100-kilogram youngster will survive.
Nature Conservation Branch officers are ready with contingency plans if the pair does not leave the beach together.
If its mum leaves it alone, the pup will be sedated and transported to a small island off Tasmania's south coast where there are two other elephant seal pups.
(la/dpa)