If you have a Preferred pet site reserved you should be in the 300 loop which is right next to the dog park so getting the puppy there would be no problem. Sites are assigned (generally) based on the size of your unit, you can however ask and see if a certain site is available at check in. There is golf cart parking at the Marina (boat to the Magic Kingdom, Contemporary Hotel and Wilderness Lodge) right next to the Settlement Trading Post there is also a cart parking area at the Outpost (check-in) bus stop as well as a small lot near the Settlement bus stop. You will also find limited (short term) golf cart parking at the Meadows Trading post and golf cart parking at both pools. Also you can ride the puppy on the cart to the dog park and there are about 6 spots there.
The Preferred sites are actually some of the tightest to get into. Since you may have a golf cart I would think seriously about a full-hook up site (1600 to 1900 also pet friendly) more room for less money, just not as close to the Marina, but closer to the pool. The premium sites are the largest and of course more money and with the puppy I would ask for 500 if you decide to splurge.
There is a mobile app "Sites at the Fort" that has dimensions of all the sites and pictures of just about all the sites.
Also check out and join www.fortfiends.net
lots of info and a good place to get questions answered.
Your are heading to our "Very favorite place". Hope you have a very Magical Time.
PS: the internal buses are very easy to use, but can be a little slow at times.