What an idyllic setting. I would love it. A person can live at least a few days without water and should be able to live a week with out food. the first priority is shelter. A simple shelter can be made with just a pile of grasses and leafs. Make a big pile and burrow into it at night. It is not the Hilton but will keep you warm at night. That will suffice for day one. Day two the priority is water.Most small islands will not have a usable water source. Look to the sea, while you can not drink sea water you can easily distill fresh water from it. Dig a small hole above the salt spray zone. You can recognize that as grasses will be growing. Use any container available to carry water to the hole Cover the hole with first a layer of twigs and over that grasses. As the sun heats the ground the water will evaporate and some will condense on the grasses. every few hours grab a hand full of the grass and squeeze out the condensed water, into each others hands if need be. It is frustrating, but before long you will get the knack and discover you have a slow but endless water supply.
Now we can think of food. You are on an island. Sea life is a banquet. Look in the tidal pools and you will find an abundance of shell fish, crabs etc. all of which can be eaten au-natruale, think sushi you would pay a fortune for this gourmet feast in any Japanese restaurant. You will also find kelp, and sea lettuce in the tidal pool. Quick rule of thumb if it is a sea plant and green in color it won't kill you to eat it. But be cautious of any red or brown plants unless you have lived on the sea and know your sea weed.
Ok, we are going to survive. now each day we do our best to improve what we have, try different means of starting fires without matches. It is actually simple if you ever took any survival training or lived in the woods or grew up as a farm boy who used to sneak off to try to smoke corn silk.
As you learn to live with the land, you will discover it will feed and clothe you and take care of you. All that is asked is you remember Allaah(swt) and do your best to live the most pious life possible.
Once you have secured your survival, form plans to contact any would be rescuers. Dig out messages in the beach sand, Prepare signal fires to light, Look for shiny rocks to pile in piles in hopes a passing ship will see them glistening in the sun light.
Now, sit back, enjoy the pleasures that surround you and give thanks to Allaah(swt) Until you are rescued, enjoy your stay on the Island and be grateful for this time to really enjoy life.