Although Google automatically saves backups of your contacts it wont save elements like your call history. If you don’t want to loose your call logs you can use the free Google Play Store App Call Logs Backup & Restore. The App has some very basic functionality and allows you to backup your call log to your internal storage. Always remember to copy the backup file to your pc before you start to modify your device. With Call Logs Backup & Restore its also possible to copy your call history to a completely new device.