How can I safely jar up my homemade salad dressing?

If you're going to sell it, you need to consider "legally" as well as "safely" (here, as in a number of situations, they're related). Check out the report "Cottage Food Laws in the United States" from Harvard Law School, or this report on the California Cottage Food Bill. Basically, with limitations, you can create and sell "non-hazardous" foods in home kitchens, but the phrase "non-hazardous" means different things in different jurisdictions. For instance, the Harvard Law report says that the 2009 FDA Code lists the following as potentially hazardous foods:

meat, poultry, and eggs; fish and shellfish; cooked vegetables; dairy products; mushrooms; cut melons; unmodified cut tomatoes or mixtures of cut tomatoes; untreated garlic?in?oil mixtures; baked goods subject to spoilage (such as cream? filled pastries or others that must be refrigerated); reduced sugar jams and jellies; pickles and salsa; and, raw seed sprouts.

The basic theory seems to be that "cottage foods" must be intrinsically safe, so that even with poor preparation and storage they won't result in a dangerous product. So, even if you could make your salad dressing safely, if someone could potentially NOT make it safely then it probably wouldn't be considered a legal "cottage food".

The California Department of Public Health gives a long list of approved foods, and none of them match your dressing idea.

The Wikipedia article gives the primary ingredients of Miracle Whip as water, soybean oil, vinegar, high fructose corn syrup, sugar, modified corn starch, and dried eggs. It also includes potassium sorbate, but I'd still be concerned about the resulting product's safety, and your lawyer may as well.

(Not a lawyer or a food safety expert, YMMV, void where prohibited, use no hooks, etc. etc. etc.)