Okay, so I thought you were in the wrong COUNTRY!
Actually, your route would be easier than ID/WA. Two hundred miles would probably be doable. The pioneers went 1800 miles, mostly on foot.
Take the same gear you would use for a long hike, with extra socks. That extra pair of boots that was suggested would be good, too. Lots of firemaking stuff, a lot of water purifier tablets or a good-sized pot, a good waterproof poncho and a hat (an attached hood obscures your vision at a bad time). A tarp for shelter, you're going to need some quality rest where you can stretch out.
Stick to the main road whenever possible. That's where the (few) people are, and the road is easier to find if you need to call for help.
Take it easy! The early settlers traveled by oxcart, at two mph (3.2 kph). Perseverance over speed. Stop and rest enough. Stop at the small towns and chat. Be willing to lend a hand along the way. Someone may be driving your way and be willing to take a passenger.
Just remember that if your family is at home, what has happened has happened. They have probably dragged the necessary stuff out of the house (if affected) and are living on your stored food. Killing yourself to get there won't help anything.
Sue