I've assembled a first aid kit for my dog and use an LL Bean "personal" sized cooler to hold everything.
Works great, has a nice carry handle, pockets on the sides and front and a handy shoulder strap. REI's personal cooler is a bit taller and would work well, too.
http://www.llbean.com/llb/shop/63702?feat=cooler-SR0&page=softpack-cooler-personal.