Here's a pure jQuery solution, but it's rather messy:
var div_height = $(this).height();
var vertical_div_top_position = $(this).offset().top;
var lastchild_height = $(this).children('p:last-child').height();
var vertical_lastchild_top_position = $(this).children('p:last-child').offset().top;
var vertical_lastchild_bottom_position = lastchild_height + vertical_lastchild_top_position;
var real_height = vertical_lastchild_bottom_position - vertical_div_top_position;
if (real_height > div_height){
//overflow div
}