Hi S.. I love the image of your dog being so gentle w/ your playful 15 mo old, and I really love how you want to add another pet to your family!
I've always had cats, but I'd like to have a dog or 2 someday. Kittens are basically like toddlers...very active, into everything and chase/pounce anything that moves. I adopted my 2 12 y/o cats as kittens before I had children, and thank goodness! But kittens ARE adorable, and use the litter box, but are active at night...this may annoy your dog. Kittens teeth are very sharp, as are their claws so if you do decide to declaw they do have to reach a certain age which I forget. A kitten will prob chase after your toddler son and bat at your dog's wagging tail, using these teeth and claws in play. It's all fun and games to a kitten, that's why I got 2! But this quickly passes.
There are many beautiful adult cats (still young, age 1 or 2)waiting to be adopted, and have established their personalities (good w/ kids, dogs, lap cat, playful, lazy, etc.) You may want to consider this. My cats now are sweet companions to my 9 1/2 y/o daughter, they cuddle w/ my 3 y/o twins, are still very playful and healthy (please keep cats indoors and spay/neuter!!)
I'm no expert w/ dogs, but I have a fondness for pugs and I hear they are good w/ kids and other pets.
Stores like PetSmart often feature cats from your local Humane Society, so take your children there sometime. Many pet shelters cover the cost of spaying/neutering in their adoption fee. My black male cat practically chose me by reaching his paw out to me, and his tortoise-shell sister got herself a home just by her gorgeous looks. I just told my daughter today "people who don't bring pets into their home really don't know what their missing." I think they're just missing something in their hearts.
May your family be blessed!
K.