Kunena is not a problem, but you need also the Joomla user database tables. Otherwise you have a forum without the corresponding members. But Joomla 1.5 has a other database structure as Joomla 2.5 or 3.5. Therefore you must migrate your Joomla.
docs.joomla.org/Joomla_1.5_to_3.x_Step_by_Step_Migration
1. Create a complete backup
2. Export all Kunena tables from your old installation
3. Copy the folder kunena "root/media/kunena" (he contains avatars and attachments)
4. Migrate youur Joomla installation
3. Export all Joomla user tables from your migrated installation
5. Install Joomla 3.x
6. Create again a backup
7. Import all kunena tables and the Joomla user tables in your new Joomla installation
8. Change the prefixes (the same as in the new installation)
9. Check in backend "Extensions -> Manage -> Database" if everything is correct
10. Install Kunena
11. Joomla 1.5 has another user management as Joomla 2.5 or 3.5, therefore you must determine new the access for all categories manually after the kunena installation.
