Hi,
I am sorry, there is no tool for exporting bookmarks. It is in our plan but I cannot tell you when it will be added into the product. It is question of priorities.
You can backup bookmarks manually. Go to profile folder: %ALLUSERSPROFILE%\AVAST Software\SZBrowser\profile\YOUR_USER_NAME\
...and backup the "Bookmarks" file. You can override the file in the future in case of any problem.