Is there a way to create a circle P or copyright symbol using the Design Online submission method?

Yes!

After saving  your quote, you can click on ART in the saved project. 

Click on Text - Add Text

Click on the Fonts (defaults to Arial) and use the drop down to select the common logo font listed just below Comic Sans MS and above Courier New fonts.

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To add the most popular symbols used on CDs and DVDs to your artwork, just add a new text layer and select the Common Logos font (looks like symbols). Using the "Common Logos Key" to the right you can then add the symbols you need in your design.

 

You can also try entering Alt + 0169

Example: 

Add a new text layer
double click on the layer and Cntrl A (Cmd A on a Mac) to select all
delete the word Text and type P
click off the layer and then back on again – Control A to select All
change to the common logos font and the circle P shows up