Did a bit of searching on the web, but no result. Then I opened the file wp-include/link-tempalte.php.
On line 1327 you will find next_post_link
which calls adjacent_post_link
function.
This function again calls get_adjacent_post
function to retrieve previous post data.
Looking at the source, you should be able to do the following:
$in_same_cat = false;
$excluded_categories = '';
$previous = true;
$post = get_adjacent_post($in_same_cat, $excluded_categories, $previous);
echo $post->post_date;
This is not tested, but I think it hould work.