As far as I remember, Blackberry announced that they are not gonna focus on tablets, so if you're learning QT, I would not recommend going with Blackberry Playbook.
Blackberry did a great job with support Qt, but they are not a strong player on the tablet market to consider them as primary platform.
As for Symbian, it's losing market and it's not gonna a major player/system. Still a lot of phones running Symbian, but the amount is decreasing.
If you're learning Qt, I would suggest going with standard desktop apps and then try Qt Android. Qt Android has some issue, but definitely Android is the main mobile platform to focus on.