Purée watermelon, lime juice, lime zest and sugar in a blender until smooth. Pour through a fine-mesh sieve into a 2-quart saucepan, pressing firmly on the pulp until all the liquid has been strained and discard remaining solids. Ladle about ¼ cup watermelon juice into a small bowl and set aside.
In a sauce pot combine watermelon juice and rose water. Bring to a boil over medium heat, stirring to ensure the liquid does not scorch on the bottom.
Add cornstarch into the reserved ¼ cup watermelon juice and stir to dissolve. Whisk mixture into the boiling watermelon juice. Reduce heat and simmer for about 3 minutes or until the sauce thickens and the liquid is no longer white from raw cornstarch, stirring and scraping the bottom of the pan with a heat-resistant spatula to make sure nothing is sticking to the bottom of the pan.
Pour pudding through clean sieve into a bowl. Cover with plastic wrap and chill until set, at least 3 hours.
Just before serving, beat heavy cream with remaining 1 teaspoon sugar in medium bowl with an electric mixer until it just holds stiff peaks. Top pudding with whipped cream and optional garnishes.