Buy a Blackberry Passport - they run most Android apps without issue these days.
Some older Android phones with QWERTY:
http://thedroidguy.com/2014/03/top-7-android-smartphones-physical-qwerty-keyboards-87556
Some Blutooth keyboards for Android Phones:
http://www.geeknaut.com/bluetooth-android-keyboards-07192518.html
If you don't see what you want - and you are that confident that other people will want it too - there is Kickstarter.com
