That hat is just darling! I especially love the unusual way each the flower's base is made of the same white straw as the hat. I would date it, as you said, to around the early 1950s. The hat elastic is not actually part of the hat, but was added by the wearer, the milliner, or the person working in the hat shop where the hat was purchased. These hat holders or hat elastics were sold separately and were used from the 1930s to the 1960s and even today. So it could have been added at any point along the way. The most common ones had little sharp metal points that you pushed through the hat's inner ribbon, after which you would break off the little sharp metal nub (though these often remain intact).
Yours is a very pretty hat.