Turns out this is unrelated to Qt after all.
It turns out the framebuffer console (fbcon) was running on my board. There is a cursor_blink setting for the fbcon and it needed to be set to 0 in order to not see the cursor show up.
I thought it was related to Qt version because when I was running the Qt4 application from TI I didn't see this, but it turns out they ran a script first disabling this.
By adding the following:
echo 0 > /sys/class/graphics/fbcon/cursor_blink
Into my init.d script, I was able to get rid of the cursor.