It will be fine. I have travelled with all of my DC from being just weeks old and transatlantic from the age your DD will be. Priority is to be sure the cot will be provided at your accommodation. Take a lightweight pushchair with a decent large UV blocking parasol. Other than plenty of clothes and the usual happy gag stuff, I would take:-
Bottle or sippy cup for water- make sure you choose low mineral content bottled water when you get there. She will need plenty of extra fluids.
Steriliser- you can get travel steriliser bags. Have tablets in and you just fill with water and hang somewhere in the hotel room.
First aid kit- thermometer, Calpol & Ibuprofen sachets,rehydration sachets, plasters etc.
Hypoallergenic factor 50 water resistant sun cream. A UV suit and 'legionnaire' style sun hat with a flap at the back.
Travel wash or some washing powder tablets- you can then hand wash stuff and hang it out to dry.
Pre-packed finger foods- for the journey and handy for when you are out and about.
Feeding spoons-handy and easy to pack for the journey. If you use them, baby foods in Europe and pretty much the same and can be bought from shops and pharmacies.
Really, don't worry. Just be sensible with the heat, fluids and food and it will be fine. You will be able to buy anything you forget or run out of in Cyprus anyway.