Add a display by copying settings from another display in Views
If you want an exact copy of the page, you can clone the display.  In Views 3 on Drupal 7, you do this by opening the view to edit it and clicking the downward-pointing triangle next to view page above Advanced and choosing clone page.

EDIT: Sorry, missed that.  By default, Views will use all applicable settings data from the Master display (hidden by default in Drupal 7).  So your content pane should inherit whatever the settings are in the Master display, which will be the same as those for the first display you created (the view in the first row) in that view, assuming you didn't override anything.  (note that some things may not apply to content panes when moving from a page but your fields, relationships, etc. Should definitely be pulled in by default under normal circumstances.)

To make the Master display visible so you can see if there's something going wrong with it, you can visit admin/structure/views/settings and check Always show the master display.

It sounds like you have multiple displays and the one you want is not the master display.  I don't think there's an easy way to copy settings back to the master display so your best bet is probably to make the master display visible and reset it to what you want before making more displays.