Kings Bay is a small residential community of larger and more expensive homes located on the waterfront with access to the Deerfield Marina. The homes sit on large lots and many have pools, but sadly, this is not a very walkable community as there aren't any sidewalks for you and Fido to walk on. You are stuck with walking on the streets unless you want are a member of the country club where there is a walking trail that runs all the way around the golf course and, even then, you may find that dogs are not welcome.
As for restaurants and any kind of store, including ones that sell pet supplies, you won't find them within the community. You'll have to cruise out to US 1 before you start your search. One great perk of the area, however, is that the weather is fantastic. You'll be able to walk most days out of the year without a problem.
Despite being a luxury home community, the terrain here is not that much different than you might expect to find anywhere in Miami. The ground is flat with a country club and golf course wrapping around a large part of the neighborhood. Going for walks around the neighborhood means walking on the streets as there are no sidewalks to utilize. This means that you need to take extra precautions on your walks such as wearing light-colored or reflective clothing to help motorists see you. It also means walking against traffic and paying close attention to what is going on around you.
Of course, you can always take your pup walking along the dirt trails in the Ludlam Pineland Preserve where both of you are sure to enjoy strolling out in the fresh air among the Pineland scrubs and along the waterfront where you can watch the activities in the bay.
Within the community of Kings Bay, there aren't any greenways, but outside of the community, there is the golf course with a walking path running all the way around it. Be sure to check with the Deering Bay Yacht & Country Club to see if you are permitted to walk your dog within the boundaries of the golf course.
Just to the south is the Deering Estate North Addition Preserve located on the site of the home of Charles Deering, a Chicago industrialist, who was an avid environmentalist and preservationist. Throughout the estate are trails to follow and the site of the Cutler Burial Mound, one of the few prehistoric burial mounds still in existence. This is an excellent place to take a walk, but you must keep your pup on a leash and you should bring fresh water for them as there aren't any facilities within the preserve once you move away from the small community within.