After repeating the last segment of the movie couple of times i have concluded Travis is the one to bring the infection inside the house.
Explanation:
Right after the table segment, where the families decides to not communicate with each other, Travis had a dream. In his dream he finds himself heading through the red door. Travis picks up a gun from the woods and heads deep eventually. Then he notices the dog bark in fear and also the presence of some other creature which might have infected the dog. This scene was again repeated right after he gets infected, while Travis lays in bed and he closes his eyes for the last time. These two scenes indicates that Travis was the one who Opened the door in his sleep to go to the woods to find the dog. Once found, He took it back home, where everyone finds it later. By this time Travis is awake and conscious and upon discovery he finds himself having to deal with the death of his dog.
Now for Andrew, kids always love to run around the house and sleep when they want where they want. The same thing happened to Andrew, and he ended up in grandpa's room. When Travis was conscious and curious, before the door was found open he touched Andrew and took him to his parent's room. This part definitely took place right after Travis rescued the dog with his subconscious mind as a result infecting himself. Andrew did not venture through the red door or touched the dog himself, as a kid he wont have the knowledge to wash his hand or wear gloves after a high possibility of blood stains from the dog.
PS. At the beginning of the movie Travis's mom was concerned if Travis after his grandpa's death, His parents also had a brief conversation about his physiological state that gave a vague idea about something being wrong about Travis.