Geologists generally accept that there's 2 varieties which are known as Rose quartz; the more common form which is found as a large undefined mass (used for making tumbles, carvings etc) and the rarer, highly collectable, crystalline form. Early assumptions put the colour of Rose quartz down to Manganese, Titanium, Iron and even Rutile within the crystals but modern research builds upon these ideas and has even come up with a new theory.
Some geologists have argued that the crystalline formation should just be known as pink quartz as it can have have different physical appearances and have different causes for the colouration. Most of the time in this formation though, it is due to irradiation of either Aluminium and Phosphorus in the lattice structure.
The massive formation, which geologists agree to call Rose Quartz, is a different story. It has been tested thoroughly by techniques such as X-ray diffraction, Scanning Electron Microscopy and Infrared spectroscopy. They found the colour of Rose quartz appears to be down to the nanoinclusion of numerous fibres within the crystal. The testing of these fibres showed that it is very similar to Dumortierite but does not match exactly. It's been proposed that it's very closely related and given the name dididumortierite.