I have the same carrier Claire, they are really good.
Although I`ve only transported mice and dwarf hamsters in one and not a Syrian! What I normally do, is line the carrier with some fleece (I have a few bits and pieces from when I made hammocks for my mice) and an egg box with holes in it for the wee one to hide in. My vet is only a short five minute taxi ride away, so I don`t bother with cucumber or a water bottle, but on a longer journey it`s probably better to take these, just in case of waiting times in traffic or the surgery itself.