hey there!
for stuff like this, i usually go the route of using the wordpress export tools (Dashboard-->Tools-->Export) and export everything
then over on the dev site i install the wordpress importer and select the newly generated export file
during the import, choose to import all media too if prompted
this should allow you to install the new theme and play with it with your real content.
it's not synced, so before launch you'll either need to reimport or hand propagate your edits
if you want me to delve into any pieces here just let me know!
good luck!