If you have one, a very large rubbermaid tub or two with a homemade wire mesh top works great. I've used this before to transport birds.
I simply took a piece of mesh larger than the tub, formed it into a rough 'U' shape (so the short sides of the U were wrapped around the sides of the tub) and took a pair of straps (used to attach the bikes to the car for vacation) and wrapped around the whole thing - to keep the birds from knocking the top off in mid-drive.
One thing I find VERY helpful is to use a LOT of pine bedding in the bottom of the tub. Helps to minimize odors, especially if you cannot have the window's down! Otherwise the stench is enough to knock your knickers off! Pewwwwwww.....
Good luck!
edited to add: if you're planning on using cardboard boxes - see if the facility will allow you to dispose of the boxes there. You DON'T want to take those stinky boxes back home! Trust me....1hr is plenty long to sniff that smell.....