I am looking for a dog friendly garden weed killer and am thinking of a home brew of a saturated solution of common salt with a good glog of washinh up liquid

Don't know where the weeds are situated but what I do so my dog can't get to anything that I have sprayed with weedkiller in my borders is to cut the bottom off a fizzy drink bottle, place it over the weed pushing it into the soil a bit then spray through the top opening. I then put the lid on. Also doing it this way means I don't get any weed killer on my other plants. If your weeds are on a pathway then sorry, this not any help but maybe another member will know of something. Welcome to GOY. :-)

Using a saturated salt solution is a way to kill the weeds - unfortunately, it will also poison the soil for some time, including the micro life forms in the soil which keep it healthy and functioning, and any plants you want to keep may also die. Salt saturated soil takes anything between 4-12 months to recover, depending on rainfall. The fact salt and washing up liquid are in your kitchen does not mean they are innocuous substances if improperly used.

The most dog friendly solution is using a fork and digging out the weeds, where possible.

A saturated solution? Crumbs that's very strong! Avoid weedkillers where possible - get it cleared by hand and keep it clear by daily checks and/or hoeing. Gardening isn't a one off and sit back, so killing them all off with any weedkiller is only temporary. And spraying weedkiller can damage other plants if there's the slightest breeze.
And should you ever want to spray against insect pests with a weak solution of washing up liquid make sure you use an eco brand.
You can't have a garden without weeding....

Know what you mean about using weed killer but I've had to resort to using it on my Horsetail :-(. Think it is the only way I will ever get on top of it.

That one breaks all the rules Jen!

Lol, it sure does, if you try and dig it chance just making more grow.