Good news & Bad news.
Good news: wonderfully easy to do. Yes it really is as simple as whip stitching together two scarves.
Good & Bad news: finding two scarves that are identical outside of a retail store are slim & none. If you want front & back identical, you might as well buy the one you linked because you might spend more on the individual scarves that that dress is selling for.
If you don't mind front & back not matching, estate sales and consignment shops that sell better quality used clothing are the way to go. I have picked up real Gucci scarves (easily $50 new and 100% silk) at estate sales for a dollar or two.
More bad news: if you want it to be a dress
I hope you are short in the torso and/ or under 5' 5". Real scarves just won't be big enough to cover decently to be a dress if you are any taller than that. As a blouse of course it'll be fine for any size. That company (most likely) prints the fabric in a scarf motif, but in sizes actual scarves don't come in in order to have it look the same on all sizes that they sell.
Hope that helps, it's a very cute idea