Move or transpose entire piano piece up one octave.

Welcome aboard...

Try this:
Select all the measures you wish to correct - i.e. click on the first measure, then shift + click on the last.
Now, with them all selected, use Ctrl + up (arrow) to raise one octave.

Alternatively, you can right click on a note, then Select -> All Similar elements in Same Staff.
With the notes selected, use Ctrl + up.
Regards.

Or, the standard shortcut Ctrl+A to select all.

To select all of a stave (or all, form this measure onwards):

Left - Click on measure
[Ctrl][Shift][End]

Then [Ctrl] UpArrow to transpose up an octave.