Q.Lawn fungus
Just had sod put in. We have had a very wet summer in central FL. so the sod was very wet when laid. It started to look as is it were dying. My landscaper said it was fungus from all the rain and it should be treated. We have dogs so I want to use a pet friendly product. I made the baking soda/veg oil/liquid detergent mixture and sprayed the lawn. How often should this be done and when would I start to see results if it is working? What results should I see?

Though you can treat many fungus issues, the fact that your lawn is newly laid sod, may require a professional to look at an diagnose the best treatment plan.
Here are some links for you.
https://www.gardeningknowhow.com/lawn-care/lgen/grass-fungus.htm
https://www.gardeningknowhow.com/lawn-care/lgen/treating-lawn-diseases.htm