My DD hated the sungli too, I did much better with my 2nd DD when tried a few other carriers.
A good stroller and a good baby carrier is a great plan. Bring your own stroller from home, the park ones are not good for babies and you will want it out of the parks too. If it folds down and is light that is a bonus for buses. Having a rain cover is a good idea too (especially during rainy times, winter it isn't as vital but can save a trip if a front comes through.)
We liked to have our DD's favorite blanket and soft toy with her, it helped to comfort her when she felt away from home the blanket was great going from hot to air conditioning (or to cover her up from any splashes on rides.)
If she uses pacifiers bring a bunch. They only sell one kind on property and if it isn't the kind your kid uses you are out of luck.
Are you breast of bottle feeding? That makes a big difference in feeding. We never bothered with any extra food at that age (my kids started solids older) but some finger foods can be good to keep them busy or to chew on if teeth are bugging them.
Best of luck. We took my 1st DD at 8 1/2 months and her sister at 7 months and 9 months old (those were the 1st trips of many, they have both been 12 and 6 times now.) They are 3 and 6 years old.
You might want to have your child try sleeping in a pack and play before hand to get used to it. Bring a lot of blankets from home some it smells like home. Bring a lot of changes of clothes and layers. I liked the all in one things for that time of year in the winter. Didn't have to worry about the socks and shoes falling off.
Best of luck and have a great time! Take lots of pictures!