We took our DS to the USA at 9 months old for a month and last October we took both DS and DD (aged 3 and 15 months at the time) to Phuket for a week so I will try to answer some questions for you.
1. We took nappies and wipes with us to Phuket. We didn't really take me stuff over as it's so hot and we mainly packed summer clothes and swimming gear so plenty of room in our luggage.
2. Both our two were on formula when we travelled. We packed two dispensers full of formula for our hand luggage and took empty bottles on the place. We asked the flight attendants to fill them with boiled water so they could cool. Otherwise bottled water will be fine - your DS will be almost one by then anyway. We also took one made up bottle on the plane with us as drinking a bottle for take off and landing helps children "pop" their ear pressure. We had no problems with security etc. I'd take a full can of formula in my luggage plus a dispenser in the plane - the flight to Phuket is not that long (compared to our trip to the US when we were in transit for 19 hours).
3. Pack some solids for the trip plus some extras but you will be able to buy them over there. The sachet packs (Rafferty's etc) are great because they reseal and they are lighter than cans, won't smash like glass jars. Also if you forget a spoon they can eat straight from the sachet.
4. We didn't need any extra immunisations for our trip to Phuket.
5. Flight was fine - DD slept most of the way (noise of the plane soothed her) but otherwise plenty of little things to keep him distracted, lots of snacks, that kind of thing. For our long flight to the states we used a wrap to strap DS to us to sleep. I couldn't relax when he was in the bassinette because I worried he'd wake up while I was sleeping, try to get out and fall. In the wrap we could both sleep together. We didn't use any medication (though we took panadol with us in case of fever or teething pain while we were away).
6. We took a pram - it was fine and didn't get damaged. We did take a cheap umbrella style pram (that still reclined) just in case it was lost or damaged and because it was lighter and easier to cart around - but we had no problems.
7. Most restaurants in Phuket have highschairs anyway - we ate lots at our hotel and it was very kids friendly. Otherwise we sat DD on grass near the pool, held her on our lap, sat on pool lounges to eat etc. Very casual and easy to feed without worrying about the mess.
8. We didn't order a baby seat - just took DD in the seat with us. Made me very nervous but it was fine. We also went in tuk tuks with her. Not sure why I felt that was ok - we are extremely strict about car seats here. However you should be able to take both a pram and a car seat with you (check the conditions of your ticket) and the cars/large vans we went in all had anchor points - you could request one especially. I think we didn't worry as we didn't take a carseat for DS to the US as it was completely impractical - we mainly flew or trained around the states and there is no way we could have managed a car seat as well (plus we only would've have used it for 3 short drives).
9. I would persevere with water. He will drink more if he is thirsty over there. You can also offer him watery foods (like fruit plus adding water to any purees etc). Just remember to only drink bottled water (you guys as well).
10. Baby sling? Otherwise check if you can borrow/hire a pram in the airport or if you can put your pram in the actual plane. We were allowed to for one part of our USA trip - DS slept in Hong Kong airport in his pram for hours - with me asleep on the floor hugging the pram and his feet (in case anyone tried to take him out!
Phuket is a great place to go with kids - we really just lazed around the resort, watched fireworks on the beach and relaxed. The people there were so friendly to the kids - to the point DS kept asking why everyone wanted to be his friend. They were really helpful every time we went out to dinner etc - I had to tell the waitstaff that they didn't have to entertain the kids for us as I felt bad that they were already working hard enough. We stayed away from the rough nightclub areas and the shopping was pretty boring (unless you like 3000 stalls of the same knock-off stuff).
Travel is a wonderful gift to give your children and I think starting young is great - our trip this year is to drive from Perth to Tassie and back again. If you need any extra info about Phuket just ask.