My friends w/ small dogs that take them on bike use front baskets. You can keep your eye on your pup while young and interact with your dog while riding. Racktime products are well designed and good values. Owned by same parent company as Tubus. Most of your bikes have midpoint brazeons and cushy tires. Snapit adapter lets you easily remove the entire basket quickly and attaches securely. You can use a small blanket and have room for toys. Make it puppy friendly, maybe add some flowers....
My dog is a female Redbone Coonhound. She weighs about 75lbs and has to run beside me in low traffic situations. On the leash in trafficy situations. She used to ride in a Burley kids trailer when a pup, but no way am I lugging 100lbs behind me so that she can have a free ride.
Racktime Baskit
Racktime Topit Front Rack