I have had this working in PC-BSD and I agree: it is a great little browser. It worked flawlessly for me.
In FreeBSD, however, I haven't been able to get it to work yet.
I followed exactly the same simple steps which I used for PC-BSD and which are listed on the QtWeb Browser website IE download --> unzip --> make executable
But this hasn't worked for me yet under FreeBSD.
Does anyone know why that might be?