This is the normal recommended approach although a properly insulated foundation or non-frost suceptible fill may be alternatives. If there is a step down below the door, even if heave takes place, it might not be critical to the proper functioning of the door.
I would recommend that you check with the local building inspector.
Clarification to this question is that the stair is being supported by existing porch framing which do have footings that extend to frost depth. The support for the bottom of the stringer is the part I was wondering about.
A simple way to do this is with concrete piers to frost depth.
If the stringers are simply placed on a slab, if heave does occur the stringers will just rotate, although the connection at the top might work loose over the years.
Make sure you don't set the stringers directly on the concrete, it will rot. Use a Simpson standoff or similar detail.
