The easiest way to do this is to use sync. Log in on the computers, go to bookmarks and click on "other speed dials".
There is no export feature, but you can copy the file manually if you want an alternative to sync.
Go to this folder: C:\Users*username*\AppData\Roaming\Opera Software\Opera Stable
If you use opera beta or developer, change to the right folder instead. Then, copy the file favorites.db. Use an USB stick, cloud service etc to transfer the file to the laptop.
In your new laptop, go to the corresponding directory, delete the favorites.db file there, and paste the favorites.db file from the other computer. Note that the speed dial entries you have there will disappear.
Then restart Opera.