Preheat the oven to 350°F. Form the cookie dough into a large ball, then roll out into a flat circle on a pizza pan. It will expand, so make the crust slightly smaller in diameter than your pizza pan. Bake for 12-15 minutes or until the crust turns slightly golden.
While the cookie crust is baking, whip the cream cheese for 2-3 minutes on high until it is smooth. In a separate bowl, whip the heavy cream until it becomes stiff and peaks form. Fold the whipped cream into the cream cheese and add in the powdered sugar and lemon zest. Mix well until it's smooth and creamy. Cover and let it chill in the refrigerator.
Remove the cookie crust from the oven and let it cool for 15 minutes. You can place it in the refrigerator so it chills quicker. Once it's cool, spread the icing over the entire crust. Decorate the pizza with circles of alternating strawberries and blueberries, whatever design you desire. Serve immediately. Cover and save the leftovers in the refrigerator for up to five days.