The only ingredient in that recipe that would spoil quickly is the shallot. Since the dressing contains quite a few ingredients with preservative properties (vinegar, soy sauce, olive oil), the dressing will likely last a month or more without any issues.
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Garlic + Oil = Danger Same issue with the shallot. 3-5 days, a week tops.
You can read more about the subject here:
http://umaine.edu/publications/4385e/