Portia - we are going to Majorca in 4 weeks and have 2 dd 2.5 and 15 mns, and I know how you feel regarding the doubts - its because you are trying to think of all the things you need etc !
We took dd1 to Cyprus at 4ms and found that local supermarkets did a wide range of jars of baby food - I know your dd is 1 but sometimes it is easier to take a jar esp if going out for the day, and also sold Pampers etc. Agree with lou33 about sterilising - I also did it in a bucket with tablets - they are light and easy to pack, and I bought a bucket over there. Or you could just boil the bottles.
If dd is onto cows milk, that will make it easier, as most restauraunts will fill up a bottle and heat it for you, if dd is still on formula, as my dd was, then I took the formula with me as I don't think you will be able to get UK brands in Skiathos - you will be able to get some type of formula though - I packed the tins in the hand luggage just in case I lost the case !
We took the umbrella type buggy right up to the gate, and the crew put it in the hold at the last minute - great as you can push dd round the duty free for those last minute duty frees !
Also found parasol attached to buggy essential, and maybe take a back carrier if you have one as both our dds loved theirs, and would sit for ages in them, good if you go for a meal or drink, and you can attach a parasol to some of them - looks a bit silly but let dh carry it !
Don't forget to take food/drink for the flight - and allow for any delays - you may want to take a small cool bag with her food in which would also be useful over there.
You can buy lots of cheap buckets etc, and things for the pool - inflatables etc out there.
You may want to take aquanappies as some pools require them, or mothercare sell swimming pants that are a nappy - reusable for about £7 - good because you get through a lot of aquas as they are always in and out for short periods of time !
I also would take a bit of baby food to tide you over until the shops are sussed out, and maybe a thermos - to heat jars/bottles whilst out.
Well, I've gone on a bit ! Better do some work - I'm in the holiday mood now!
Oh and don't forget her passport..!!!!!