You can save your design as a template then load the template into a new board with a larger board outline. To do so, select File Save As Template. Give the template a name and select ok. Create a new board then right click on thelayout areaand select load selection. The only issue that you will run into is only the layout is saved. The schematic is recreated automatically. If you did not start from schematic, then you are all set. If you do have a schematic created in PCB123 this may not be the best option. Copy and paste of either the schematic or layout will have the same effect. Only the side that you copy will be maintained.
Rather than copy the work into a larger outline I would save the file off as a new name then make the outline larger and modify the design. This would maintain any schematic work and allow you more room to complete the layout. If you are not familiar with editing the board outline the following should help.
PCB How To Edit PCB's