Certified GKH Gardening Expert
If you are killing weeds, the normal vinegar that you buy from the store will do. There is no need to dilute it as it is already diluted when you buy it. And, the vinegar from the store will not harm your dog. Here's a recipe that may help using 1 gallon of white vinegar, 1 lb. table salt, and 8 drops of liquid dish soap. Mix the vinegar and salt in a pan on the stovetop. Bring to a boil so that the salt dissolves into the vinegar. Remove from stove and stir in the dish soap. Allow the mixture to cool. Pour into spray bottle and use a stream setting to aim directly into the middle of the dandelion rosette so that you do not kill the surrounding grass. Dandelions should die within a day and it won't harm your dog.
This article should help as well: https://www.gardeningknowhow.com/special/organic/homemade-pet-friendly-weed-killer.htm