Can my dog walk through my natural made weed killer?

Dish soap is not safe for dogs!

CAN the dog walk through the mixture?  Yes, it CAN.  I wouldn't allow my dog to walk through salt and vinegar, but I don't know if it's dangerous.  I'd be afraid she would lick herself and absorb the vinegar.

Yes, Round Up should be taken off the market.  I got into a screaming match with the landscaper for my HOA, because he was using Round Up on public areas. He isn't using it any more!

Yes, your dog will be fine but from my experience, that solution doesn't work unless you use commercial grade Vinegar & spray upper leaves & under the leaves.  I just found it best to cut them at the roots & just keep them down.  

I have a half acre & dogs & a yard full of weeds.  When they get bad I take down the huge one & let the little ones stay.  It is hard to keep a yard free of weeds when you have animals.

If you put some shoes on the dog it will probbaly be ok