Tap the selection options icon (4th icon from the upper left) > Select All (be sure that the desired layer is selected). Tap the edit icon (3rd icon from the upper left) > Copy.
Close the project. Open or start a new project. Tap the edit icon once more > Paste. (Note the results will constrain depending on size of the new project's dimensions. In other words, it'll size to fit the new project if smaller or larger.)