Unlike in some of the adaptations, nightgowns would not have been worn around others in Jane Austen's day. In Pride and Prejudice, when Bingley has come back to Netherfield after his long absence and is about to visit the Bennet family, there is a mention of Mrs. Bennet running into her daughters' room in her dressing gown to try to hurry Jane so she is dressed and ready to receive Mr. Bingley.
Chapter 55:
"He came, and in such very good time that the ladies were none of them dressed. In ran Mrs. Bennet to her daughter's room, in her dressing gown, and with her hair half finished, crying out,
"My dear Jane, make haste and hurry down. He is come -- Mr. Bingley is come. -- He is, indeed. Make haste, make haste. Here, Sarah, come to Miss Bennet this moment, and help her on with her gown. Never mind Miss Lizzy's hair.''
Unfortunately, satin would not have been the material used. This site
http://home-and-garden.webshots.com/albu… shows some Regency-style nightgowns. This site
http://www.janeausten.co.uk/magazine/pag… shows you what might be an example of a dressing gown, which looks to be somewhat like a robe thrown over a nightgown.
There is also a scene in Sense and Sensibility, after Willoughby is married and Elinor and Marianne are still in London in which a dressing gown is mentioned. It is in chapter 32: "Elinor, with great civility, declined the proposal. Her sister was, perhaps, laid down upon the bed, or in her dressing gown, and therefore not able to come to them."
I can't think of any other scene in the books which make a mention of a nightgown or dressing gown. As I said, satin wouldn't be the proper material. However, if the teacher would overlook that, you could go as Marianne Dashwood (Sense and Sensibility) at Cleveland (the home of the Palmers) where she and Elinor stayed on their way home from London. It was here that Marianne became deathly ill and, thus, had to stay in bed. Presumably, she would have been wearing some sort of nightgown.
I hope this helps.