It's not clear to me what "baffling" problem you have that would specifically require a QTIP. Why a QTIP rather than some other kind of trust, for example? What is it that you see as the problem you want to solve?
Broadly speaking, trusts fall into two categories. The first are inter vivos trusts (what is popularly called living trusts). These are trusts that you create during your lifetime. Then there are testamentary trusts. This is a trust created after you die, typically by putting the terms of the trust in your will. You can also create an inter vivos trust but not fund it (known as leaving it dry) until your death and have the will direct assets to that trust.