Both Kate and Dolphin use the same list with entries which contain server localisations (such as FTP e.g.). This list is called "places". When you add an entry to this list, then provided localisation will be easily available in both of the mentioned programs. This article will tell you how to save (backup) this list when to migrate your Ubuntu or set up a new one.
All entries which builds "places" are stored in a hidden directory, placed in our home directory.
All you need to do is to copy from this directory this file:
Now move it to analogous place into the second machine. Additionally if you want to save other settings from KDE applications (e.g. passwords from KWallet) it's also worth to interest directories like: