As I know SuSE is RPM-based distro.
So
Qt Code: 
  1. $ rpm -qf /usr/bin/designer
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should give you name of PRM package with Qt developer's tools (in my case it is qt-devel-3.3.5-11.0.fc3.kde)

Next step:
Qt Code: 
  1. $ rpm -V qt-devel
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If your file was somehow lost you'll get a message.

Alternate way is use
Qt Code: 
  1. $ rpm -ql qt-devel | less
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for list all files from package.