The Old Curiosity Shop by Charles Dickens is replete with ideas which might be explored in an essay of some length.
First of all, you might consider a character study. Like most of Dickens's novels, there are plenty of characters from which to choose. One is the complicated character of Nell's grandfather who, on one hand, is determined to protect and provide for his granddaughter in any way he can, but on the other hand gambles away his only means of accomplishing that goal. Kit (Christopher Nubbles) is another character who might make an interesting character study, as we see him deal with love, betrayal, and devotion as he is treated unfairly by most of the people he gets close to--but is still a decent and kind person. Daniel Quilp is a grotesque and evil character; he would be fun to explore a bit. If you are looking for a challenge, see if you can find some redeeming qualities in him.
A possible theme to explore in this novel is untimely (early) death. There are many examples of this in the novel, and an exploration of what this means thematically might be an interesting study. Connected to this is the impact of untimely deaths in Dickens's own life which are paralleled in many of his works, including this one.
Another possible theme is the social commentary Dickens makes in the novel, something we see in almost every one of his works. It is certain that Dickens had a level of concern for the bigger picture of his countrymen dying too young because of hunger, deprivation, and disease. By the end of the novel, through no fault of her own, Nell has been forced to beg for food.
She approached one of the wretched hovels by the way-side, and knocked with her hand upon the door.
"What would you have here?" said a gaunt man, opening it.
"Charity. A morsel of bread."
"Do you see that?" returned the man hoarsely, pointing to a kind of bundle on the ground. "That's a dead child. I and five hundred other men were thrown out of work, three months ago. That is my third dead child, and last. Do you think I have charity to bestow, or a morsel of bread to spare?"
An examination of Dickens's social concerns as depicted by his treatment of the characters in this novel would make an interesting essay, as well. (Pay particular attention to his outrage about these matters as expressed through the characters and situations in the story, exemplified by the scene Nell witnesses at the next house where she plans to beg for food.)
Finally, some critics (Oscar Wilde among them) have called Curiosity Shop maudlin and even laughable. Perhaps you could explore the somewhat melodramatic nature of this novel. Where is the line between tragedy and comedy and does that line get crossed in this novel? One good example to start with if you are considering this idea is Nell's death. While it is certainly a needless and tragic event, does Dickens go too far in his depiction of this little girl's unnecessary death? These are some good questions to consider.
These are just a few ideas, and of course you must determine a subject which both interests/intrigues you and meets the guidelines of the assignment (i.e., research, length). Happy writing!