I hate to admit I know this, but they actually make backpacks that you can put little dogs in. I like the milk crate idea, but if the dog's not too smart, you may want to zip them inside of something. Just saying.
My first dog LOVED riding with us.. I had a front shoulder pack made for small dogs. We would ride for miles...... Sadly she died at age 14. My new dogs isn't crazy about rides.. The longest ride for her was less than a mile, then I got the "LOOK" to return home.. OMM.