As @lpb says, you can use Asana’s “Schedule Project Dates” feature; as mentioned, it involves setting up an initial set of dates in your template, whose dates relative to each other generate a new set of dates in the new project.
If you’d prefer not to use dates in your template but rather just specify durations for each task, the Dynamic Duration Workflow type in my Flowsana integration provides that capability - Flowsana adds a “Duration” column where you enter the number of days (or weeks or months) for each task, and then Flowsana uses that information, along with the dependency structure you set up, to generate the dates for your new project (and to update dates appropriately if schedules shift).