Is storing homeade dressing with garlic powder safe?

Short answer: Homemade salad dressing, even with garlic, is generally considered safe, for a time frame of up to a week.

While some strains of botulism can grow slowly at refrigerator temperatures, in general botulism requires three things to grow in addition to having spores present:

• Low salt, low acid environment
• Low oxygen environment
• Temperatures above about 35 to 40 F (depending on the strain)

Garlic is one of the foods at risk for having botulism spores present.

Your recipe is vinegar based, and so is acidic. With the olive oil, the total dressing may be under the 3% threshold that completely inhibits botulism growth—especially when the dressing loses its emulsification and separates into layers, some layers may be less acidic.

Still, your strongest protection is the refrigeration, combined with the acid, and the short time frame.

Health Canada specifies that plain garlic and oil (much more at risk due to the lack of acid) can be kept in the refrigerator for up to a week.

You can therefore infer that with the additional acid, you will get at least the same week of safety, although I would hesitate to go longer as safety issues always warrant conservative assumptions.