I think your on the right path with unit testing and its a great plan to improve reliability of your product.
Though unit testing is not going to solve all your problems when converting your application to different platforms or even different operating systems. The reason for this, is the process unit testings goes through to uncover bugs in your application. It just simply throws as many inputs imaginable into your system and waits for a result on the other end. Its like getting a monkey to constantly pound at the keyboard and observing the results(Beta testers).
To take it to the next step, with good unit testing you need to focus on your internal design of your application. The best approach i found was to use a design pattern or design process called "contract programming" or "Design by contract". The other book that is very helpful for building reliability into your core design was.
Debugging the Development Process: Practical Strategies for Staying Focused, Hitting Ship Dates, and Building Solid Teams.
In our development team, we looked very closely at what we consider to be a programmer error, developer error, design error and how we could use both unit testing and also building reliability into our software package through DBC and following the advice of debugging the development proccess.