I'm not quite clear on what you mean by a dress inspired by Meg March. Do you mean a dress inspired by what she wore in the movie, or as described in the book, or just inspired by her character?
In the 1860s, cages were ubiquitous. They were quite inexpensive, sold everywhere, and came in many sizes. Women of all ages wore them, even little girls as young as toddlers show up in pictures wearing them. The variety of sizes available, and the fact that they allowed women to obtain a fashionable shape without resorting to many, many heavy, starched petticoats, made them extremely popular, even for women doing housework.
So, despite the Marches "genteel poverty", it's likely that Meg had access to a cage. Meg as a character is very concerned with "keeping up with the Joneses", so it's also likely that Meg would have desired the fashionable shape that a cage could offer. The question becomes what size she would have worn, and whether she would have worn it all the time. As to the latter, I would argue that she likely would have worn a cage when doing anything but the heaviest of chores; for the former, that's up for debate.
This also begs the question - since the book spans many years, are you sewing a dress for teenaged Meg, or young lady Meg, or post-marriage Meg?
In regards to difference in length for cage vs. petticoats, the cages I have worn are larger than 100" but there is a distinct difference in length of at least a few inches - but again, my cage is larger.
Do not fear the cage. There is a wealth of wisdom here from ladies who have been there before and can help you through it