Sorry, no, this is not the recipe for a Blue Moon cocktail. This disgustingly sweet concoction would be enough to put a person into a diabetic coma!
The real Blue Moon cocktail is a variation of the Aviation cocktail and contains gin, crème de violette and lemon juice, shaken with ice and served in chilled a martini glass. If you Google 'Blue Moon Cocktail', you'll come up with variations on this recipe, as shown in the Washington Post:
2 ounces dry gin, such as Tanqueray
1/2 ounce freshly squeezed lemon juice
1/2 ounce creme de violette
Fill a mixing glass two-thirds full with ice. Add the gin, lemon juice and creme de violette. Shake vigorously and strain into a cocktail (martini) glass.
Adapted from "The Fine Art of Mixing Drinks," by David A. Embury (Doubleday, 1948).