I had the same problems running the tutorials after
fighting to get the code to compile. Here's what I
found: QtPerl works fine on my Mandrake 7.2 box
using Perl 5.6.0, Qt 2.2.1 and gcc 2.95.3. However, on Mandrake 8.1 with Perl 5.6.1, Qt 2.3.1 and gcc 2.96 it gives the Can't locate object method "new" via package "Qt::Application" error on running any PerlQt app.
I copied the Mandrake 7.2-statically-compiled module over to the Mandrake 8.1 box, but running PerlQt apps still resulted in the same error.