There are multiple packages capable of designing QSAR models.
At a basic level, QSAR is about building a statistical model fitting some property/activity based on a set of multiple descriptors. You can use any multivariate statistical package to do that, including R (as indicated in the other answer) or Python.
If you're new, I would highly suggest KNIME an open "platform" for connecting multiple software packages for analyzing data. It's heavily used for QSAR.
There are several examples for KNIME QSAR, e.g. using CheS-Mapper - a quick search turns up several.
A critical concern, though is validation, either through separate training and test sets, cross-validation / bootstrapping methods, or other techniques. It's easy to design models that fit noise.