There is no rule of thumb encompassing all salad dressings.
One "rule of thumb" which sometimes gets used is to look at the shelf life of the most perishable component. Frequently it works; sometimes, it is dangerously misleading. A mixture of the things you listed can have a longer or shorter shelf life of that of the most perishable component. An example of lengthened shelf life is mayo; it stays good for longer time than a cracked fresh egg, because the yolk gets pasteurized and the pH is lower. But there can be examples of the other thing happening. The classic is the homemade garlic oil: you can keep pure garlic and pure oil for months in the pantry, but once you combine them, you get a botulism risk.
I don't usually keep salad dressings in the fridge, but if I did, I would look at why the most problematic component has the shelf life it has, and decide whether mixing it will change the condition. For example, if I had a mixture of oil, vinegar and pure emulsifier: Oil keeps for months because it has no carbs, so nothing for bacteria to eat. Vinegar can have a few carbs, but not a lot, and it also has a very low pH, so bacteria die in it. The combination still won't have enough carbs for bacteria, and will still have a low pH. So the mixture will keep for very long time, just like pure vinegar or oil.
On the other hand, imagine mixing vinegar with honey and water. Honey doesn't go bad by itself, because the carbs are too concentrated for bacteria. The vinegar and water will dilute them, so this mechanism of bacteria prevention vanishes. The pH of the mixture will probably rise a lot too, because the vinegar gets diluted, so no protection on that front either. Thus, this mixture is apt to go bad much earlier than pure vinegar or pure honey.
This method requires that you make a new decision for each new dressing you make, and that you acquire enough knowledge to be able to make such decisions. If you feel this is too much effort or too risky, you can either start adding conservants to your homemade dressings, or just start preparing a fresh dressing for each batch of salad.
I make a nearly identical recipe for caesar dressing, and have safely used leftover dressing up to a week later. I can't vouch for any "technical" food spoilage rates, only that my friends, family, and I have never gotten sick from eating salad with dressing in this age range.
I can't speak to anything longer than that, as the dressing never seems to last that long!
As a closing note: if you are in doubt, don't eat it!
Best Answer
Botulism is a concern when garlic (or shallot...or even fresh herbs) is stored in oil at room temperature. An acidic environment virtually eliminates the risk, meaning that garlic, shallot, and herbs are safe in a vinaigrette (especially one that separates and has those ingredients mainly sitting in the vinegar layer), for example. Refrigeration makes the whole thing even safer. You might also take a look at this question. In general, shallot should be treated the same as garlic when considering the risks of botulism.