JWD46,
One other problem with trying to interpret CPT results in peats is that once you get through the fibrous cap, you typically encounter an "amorphous" or decayed organic zone beneath. This often is very weak material and is not soil at all, but material that looks black and definitely was fibrous once.
The problem with interpreting shear strength from the CPT in very weak soils has been covered by coneboy, who drew attention to the equipment-sensitivity problem. So, if you cannot make much use of the cone penetration resistance, you are left with trying to use the penetration pore pressure response to evaluate undrained strength. In most fine-grained soft soils, this is a much more accurate method than qc, however in your peat you may very well encounter an unsaturated pore pressure response - even below the GWT! I have tried CPT's with pore pressure measurement in such conditions and found lots of gas in the section, which partially damps out the pore pressure response to penetration.
So long as you check the response with some dissipation tests at rod breaks and use low-capacity equipment, you stand a chance at getting a decent measure of shear strength, but only within the amorphous zone.