Definitely to hard to make a really good guess on the fiber from a photo. Could be cotton or a cotton blend--if it's a blend you really do need to be careful if you can't tell what it's blended with.
I would lightly steam this with a steamer or iron on low setting--not on steam setting! Unless you have a dry cleaner you can trust to handle vintage properly, then it would be best, as Amber says, to let the cleaner handle it, especially with that velvet trim (if you do send to the cleaner for pressing, take off the buttons; I've had even experienced-with-vintage cleaners melt them....).
It's such a stunning outfit and does not look to be all that wrinkly, so the least you can do with it the better.