Two hours may not be quite sufficient, but that depends mainly on the number of third party extensions. The migration process is documented in the sticky topics at
Migrating and Upgrading to Joomla! 3.x, especially in the tutorial
Practical Guide to migrate from J1.5.xx to J3.x.
In any case, the website, the template and third party extensions will need to be reviewed before the migration can start. It would be best to do first trial migrations in a localhost environment on a workstation, running for example Wampserver, where you can easily swap between different versions of PHP.
If you need help from Joomla experts, post topics to the migration forum. You can also post your requirements to the
Professional Development Services forum with your preferred method of contact. Read first the sticky topic in that sub forum.