Hello! Costume designer here. If your party isn't too demanding, this would work alright. You've got almost the right silhouette, although the details and the fabric are wrong. You can go more or less as you are if your friends aren't historians, but I'll give a you a breakdown of what you're doing wrong if you are interested in accuracy.

First, I'd switch to a larger shawl. What you've got looks more the size of a fichu than an actual shawl. What you want is more of a square shape, and probably the size of what these ladies are wearing. I've never seen source material of a woman from this period wearing a velvet shawl, especially a middle class woman. This is before synthetic fibers were invented, so all velvet would have been made out of silk. The last time I priced silk velvet in the garment district in LA, it was $45 or $50 a yard - and that's at a discount store with modern manufacture and shipping techniques which are a lot less labor intensive than they were in 1912. Not that you wouldn't have had any velvet at all, but it probably would have been velvet ribbon used as an accent on your bodice, belt, or hat.

Next, be aware that if you go all in black, that means that your character is in mourning. Guidelines for how long a woman had to stay in mourning after the passing of a loved one were growing looser at this time, but in general if you're wearing all black that means that someone close to you (probably your husband) died within the last three years.

The necklace is straight up anachronistic. The beads are too large, and lavaleers of that type weren't really worn in that way until the 1920s. The decolletage of your bodice would likely have covered at least your collar bones, if not gone half way up your neck, so wrapping a necklace around your neck in that fashion would have looked a little odd. More common jewelry would be one waist-length necklace worn with or without a brooch at the throat. See this image for reference.

Next, the bodice and the skirt would have been two separate pieces, frequently with a thick belt worn at the waist. You can see it well on the young ladies in the back of this picture and these ladies. The older ladies in the first picture are wearing the late Victorian styles of their early adult-hood and should be disregarded if you want to play someone your own age. The shirt may have had a closure going up the center, similar to a modern day button-up shirt, and would probably have leg-o-mutton sleeves. Your arms would also probably have been covered, unless you were rich enough to afford a fancy evening dress. Isn't it funny how we take off clothes in the evening when it's cooler out? Anyway, if you want to, you could wear a white button-up shirt over the dress you are wearing in this picture, and cinch it at the waist with a belt, for a quick and dirty more accurate Edwardian silhouette.

The skirt would have been fitted with a band at the waist, and would have had pleating attached to the band to give fullness, which is one of the major details that your costume is missing. That smooth drop from waist line to full skirt hadn't really been a thing since the Romanesque Era (900-1200 AD) in 1912 when the Titanic sank, the Edwardian Era. As much as or more than the neckline, this marks your dress as very modern to my eyes.

For your hat, the shape is alright, but I'd add a few giant flowers, and/or some ribbon: perhaps a big dopey bow? You are going on a fancy-schmancy sea voyage after all. Even third class tickets on the Titanic weren't cheap, you were probably middle middle class. Some of the previous pics are good references for hat decorations. Remember, this is the generation that almost killed off all of the egrets in the US for their floaty wing feathers to stick them as accent decorations on hats.

Then, the fabrics in all of your pieces should be woven, not knits, and unless you're going for a very specific look, you probably have a plain cotton or linen on your bodice, and a lightly patterned Jacquard fabric for your skirt.

On the subject of corsets: Don't. Especially not over your dress, you'll look like you're walking around in your underwear (a shift and corset). No Edwardian woman would ever have worn her corset so that it was visible (except for maybe a prostitute). It would be worse than going out in just your bra today. Also, Edwardian corsets are very specific to the era and were designed to create a certain look, called the "S-bend" that swayed your back so that your butt stuck out a bit behind (helped by a bum roll or a bustle in the back) and moved your top portion forward. Here is a good pic. Don't do this to yourself, it's painful, expensive, and hard to find. Even most period films go without subjecting actresses to this nonsense. Besides, if you're going to corset you need to be wearing a dress that is cut to go with that style of corset, and your dress is not.

You're also going to want to try to get your hair into an updo with some volume. The popular hair style of the day was called the "Gibson Girl," decent youtube tutorial to be found here.

I think that covers just about everything! I found this article while I was looking for reference photos that might help you out. I didn't read through all of it, but the reference photos are solid and what I read seemed accurate. What you've got going will work for you if your friends aren't historians, but if you want to dress to impress you might try changing a few elements to align more closely with my advice here. You can probably rent a costume for a fairly reasonable price if you live near a decent sized city. Look for "costume house" or "costume rentals" in your area.

References:

Cunningham, Rebecca. The Magic Garment: Principles of Costume Design. Waveland Press, 2009.

Other books that I'm not dragging off of my bookshelf to cite unless you really really need me to.

Many hours of pictorial research of Edwardian clothing for design of the play Our Town. Sorry, can't upload my costume bible or reference folder without showing my real name.