PHP and MySQL (as well as a web server of your choice, my preference happens to be Apache), can be quite easily installed on a laptop. In fact, I have PHP, MySQL and Apache installed on my laptop. Installation instructions are provided at their respective websites:
http://www.php.net
http://www.mysql.com
http://www.apache.org
However, I sincerely urge you to consider the following (possible) scenario:
You run your application on a web server, let's call this the master application. Now, you have three users, all running concurrent mirrors of the master application locally, on their laptops. A week or so later it comes time to synchronize the data from the laptops (which has most likely been edited, altered, updated, etc) with the master application database. Whose mirrored database data shall reign supreme?
The whole principle of building the application and running it with a centralized database, on a web server, is to avoid this confusion. My suggestion would be to simply install a web browser on the laptop (if there's not one installed already), and have users connect to the master application running on a web server.
Just my too sense; but perhaps you have good reasons why that can't be done...