well the current Q3 which is first generation is based on MK5 Golf platform but share components with A3 Sedan.
2017 fall the second generation Q3 will arrive and it will be on VW MQB flexible platform. Shared by currently Audi A3 Sedan, TT as well as MK7 GTI. The new Q3 will be bigger and roomier. The new Q3 is less than a year away and it does not make sense to buy a Q3 at this point. The 2nd generation Q3 will be identical size as of the new VW Tiguan. Tiguan is also on MQB. The next generation Q3 will also be available with Audi new 1.4L engine.
Below is current generation Q3. ALSO Q2 is smaller than Q3. X1, GLA, Q3 compete against each other.
DSC_0188 by wahab11375, on Flickr
DSC_0189 by wahab11375, on Flickr