You'll be fine above the window with a header - the header reaches across the complete window top and you should have structure to attach to. The only area of concern would be the sill plate at the bottom. Start as indicated by previous poster at jack studs on sides and attempt to attach to the sill top stud at bottom of window that is framed out here.
Make sure to use an approved attachment with correct spacing. That’s why we attach here - the 16 OC stud spacing if attached there may not meet the needs of schedule spacing for your type of shutter. Check the shutter engineering and if it requires say 9 in OC spacing for a 50 psf in your zone - follow that schedule pattern.
In other words pre drill your hurricane panel header and sill at 9 inches on center, then attach you header to window header. Attach your sill track to wood sill plate using the tapcons or screws required. – Done.
