If you set up your new iPad using a backup from the iPad 4 it should restore the data (including bookmarks) to the new iPad. In general, newer versions of iOS can be restored from older backups. As long as you do not erase/restore the iPad 4, you can try this without risk; since you can always restore the new iPad to factory if it does not work.
It is also possible that Dolphin has settings to sync or export it’s bookmarks. Dig into them and see what you can find.
Since the iPad 4 is that far behind, expect the new iPad to do a lot of app updates after the restore. Also, not every app on it may work with the new iPad, so be careful to save important documents of files by means other than the backup, just in case.