Not walking might contribute to the problem, but lets go over some things. If you can keep a dog asleep for a longer period of time, it helps stop them from waking up so early. Some ways of accomplishing that are a small meal right before bedtime. Not a whole meal, just a snack. Dog with some food in their belly tend to sleep longer since there is no excess acid in the stomach and they won't be as hungry in the morning.
Additionally, some dogs do have a problem with excess bile, so pepcid taken at night might help a bit. Read about Pepcid dosages and usage information here: http://www.petplace.com/drug-library/famotidine-pepcid/page1.aspx
Take up water around dinner time if neither dog has kidney issues. A dog is less likely to wake up if their bladder is empty. That is a good reason to have a nice long fast paced walk before bed time. It serves to tire your dog out and provide plenty of opportunity for him to void his bladder when he marks all the bushes and trees in the neighborhood. . He may be more likely to go out if he thinks he is going for a walk. Dogs also would rather go out with their owner, so stepping outside with them while they roam around before bedtime can also make a difference.
Another thing that can help is to get a Kong chew toy with the treat compartment. You can fill it with peanut butter or yogurt and freeze it. Give this at bedtime. It will either keep your dog up for a few more hours while he gets the treat out of the kong, or will keep him occupied when he wakes up. Keep the mouth busy and they can't bark. So add a few toys and swap them out every week to keep him from getting bored.
Now there is the option of using no bark devices. These come in various forms including ultrasonic collars, citronella collars, vibration collars and shock collars. You can see these here:http://www.valuepetsupplies.com/classic-no-bark-collar-small-red.htmlhttp://www.ultimatebarkcontrol.com/vibration-bark-control-collar.htmhttps://www.google.com/search?q=citronella&oq=citronella&aqs=chrome..69i57j0l5.2403j0j4&sourceid=chrome&espv=210&es_sm=93&ie=UTF-8#es_sm=93&espv=210&q=citronella+bark+collar
I think these things will help with the situation. I would also go ahead and reward him with an extra special treat in the morning if he is able to not bark until you get up.
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Since there have been recalls on certain foods and treats, please check the following site to be sure the food your animals eat is not affected. If it is affected, contact your vet as soon as possible. Have your dog seen if they have any symptoms.http://www.fda.gov/AnimalVeterinary/SafetyHealth/RecallsWithdrawals/