Seen a few stock grand cherokees there back in May, not a problem. I saw a Hyundai Santafe driving the inland tracks and getting as far as indian head.
Tyres aren't a huge issue, the stock 18inch ones will probably be fine, just have to know that the softer P rates tyres can be more easily damaged on tree roots/rocks. So take it easy when you see them..... sometimes you don't.
Another thing to watch is the front airdam is a bit low. Not a problem most of the time, but deep washouts (where creeks run down over the beach) may see you hit the airdam.
Must haves: I'd take air compressor, tyre deflators, snatch strap and maxtrax(or similar).... oh, and make sure you have a front RECOVERY hook.
edit: We haven't had much rain recently, you will probably find the access tracks down to the beach (and through indian head) are soft, and easy to get bogged. Let down your tyres, then pump them up a little on the firm beach bits.
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MY14 GC LTD CRD-ORA2/QL|Mopar 18" Night Fever Rims&RockRails|Chief Hooks&Sump Plate|STMaxx 275/65R18
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