Does vinegar have the same function as tartaric acid in a pavlova?
I would not recommend adding cream of tartar.  Your ratio of 1 teaspoon vinegar to stabilize 4 egg whites is standard.  My personal preference is to use cream of tartar instead of vinegar if it is available to you - I'd recommend 1/4 teaspoon for 4 egg whites.

I assume you have something like 1 cup of sugar going into your meringue as well?

See also:  How much acid to use for stabilizing meringue?

Meringues bake at low temperatures for a long time.  It is difficult to provide any kind of formula to predict how baking time might increase if you double the recipe.  My recommendation would be to pipe-out your primary meringue disk along with a couple smaller test disks of similar thickness - the idea being that you can use the smaller disks to test for doneness without breaking-off a piece of your primary dessert form.  If you're planning to make a wider disk (i.e. not thicker), the baking time shouldn't vary much from what is recommended in your recipe.  Please note that the meringue should not brown - but when you break-apart a test disk, the interior should be neither sticky nor moist - the meringue is done as soon as the moisture from the eggs has baked-off enough for the result to be airy, crisp, and dry.