I boarded my dog, she was 10 at the time, at the kennel in AK. We were staying at AsMo and AKL. It was $8/day, for a guest staying on property. We had her blanket, her own food, a toy. Plus it wasn't crowded so they put her in a really large kennel. It is plastic, with a wire front. We would go over first thing in the morning, around noon, late afternoon, and then around midnight. When the park was closed - the security guards would let us in. Was nice walking around the front of AK at midnight. My dog did a lot better being with us and seeing us. When we board her at home we always get a phone call telling us she hasn't eaten in 3 days!!! She does end up eating, but she is always sick after being boarded and not seeing us. When she was at Disney - she was fine.
Where are you staying?? With a puppy, they are more flexible than an older dog. You could move the puppy around during the day, whatever park you are at, leave the puppy at that parks kennel, but at night leave the puppy near where you are staying. Just don't forget your health certificate. Oh when you leave they give you a certificate showing the dog stayed at Disney.