Here is the list of additional libs I put into my system to run Qt. Surely helpful if you are building your own!

libcrypto.so.2
libfontconfig.so.1
libfreetype.so.1
libiconv.so.1
libicudata.so.49
libicui18n.so.49
libicuuc.so.49
libpps.so.1
libslog2.so.1
libssl.so.2
libxml2.so.1
libz.so.2

Note that some of those libs are quite large. Following the "memory is cheap nowadays" approach, no one seems to care 
which libs are really needed and how big they are.

Additionally, Qt itself is inconsistent linking to C++ libs: you need libcpp.so.5 AND libcpp.so.4 AND libcpp-ne.so.5. 
But who am I to disagree? ;-)

Hope this helps,

- Malte