Some selective herbicides are definitely more toxic then others. You can see on the label if it says "caution" then it's a lower grade of weed killer. If it says "Danger" then that's the highest level of toxicity.

Most herbicides are washed off after watering or rain and become of no effect. If there was a way to (1) spray the weeds with a low toxicity selective herbicide, then (2), keep the dogs off of the lawn for a couple days, allowing the weed killer to work, then (3) water the lawn thoroughly, you should be good.

I take a cultural approach to weed control which usually does not involve chemicals. But for that I would need more information from you.

Where do you live? Please be specific down to a town or zip code.
What kind of grass do you have? I'm guessing fescue or Kentucky bluegrass.
What kind of weeds do you have?
How long and how often do you water? I'm guessing you water more than once a week.
How often do you mow and how high/low? I'm guessing you mow lower than 3 inches.
How often do you fertilize and with what products?