Camping with dog...? for a week.?

well I live in ny. an I just got my car. im 19 almost 20. and I got a puppy. is it alright to bring a 12 week puppy with me upstate. shes a small dog. I got her a dog seatbelt. this is my dads upstate property. no house on it. I use to bring my family dog up with me. we have a crate that my dad built (like a very mini cabin that we r sleeping in. I just need to grab the tools to open the front(we close it for an shimal and bug protection when we r not up there.. im not going till mid august cause my puppy is still a newborn and with her mom. but when I go she will be about 12 weeks. shes a small dog. prob gonna be like 9 pounds full grown. if it is alright what should I bring for her. I want her to get use to camping. I know to bring food. water. but im worried if the heat will get to her. her harness does have a signal on it just in case it gets to hot for the dog. I will maybe go to town with the air on in the car. but food. water. toys. leash. what else... its about a week stay. lots of walking should I buy her dog boots cause its rough terrain or no. and im bringing a lifevest cause im hiking to a nerby river. im not sure if she will go in or not. but we will see. im hoping shes gonna be a dog that likes water. any tips?