To construct a copy of segment \( PT \) using point \( W \) as one of her endpoints, Jouri must first measure the distance (length) of segment \( PT \). Therefore, she should use her compass to measure the length between points \( T \) and \( P \).
So, the correct choice is Option #3: "Using a compass, measure the distance between point \( T \) and point \( P \)."
Thus, the next step Jouri needs to take is Option #3.