According to the QuickTest Professional v11.0 Installation Guide the prerequisite version of .NET Framwork is 3.5 with Service Pack 1.
I don't know how you would've been able to install QTP 11.0 with only .NET 2 on your system.
Regardless, you should have .NET Framework 3.5 SP1. A system can have multiple version of the .NET Framework installed. You don't have to uninstall old versions. So you could have v2, v3.5 SP1, and v4.0 installed all at the same time.
Note if you only have v4.0 installed, QTP may have some problems. I don't know why 3.5 SP1 is the prerequisite, but since it is you need to have that version to have a supported environment.