It's interesting that when I started going through the many, many etiquette books I have saved to my Google Library, I found that the proper length of an engagement does not really come up frequently, except in vague terms that do not help to answer your question - essentially, "don't rush into marriage, but also don't draw things out too far; everything in moderation."

There are exceptions to the rules which govern engagements, as well as other things; but as in other cases, the exception only proves the wisdom and justice of the rule. There have been happy marriages after a few days' or even hours' acquaintance, and there have been divorces and broken lives after engagements which have existed for years. The medium, therefore, may be considered the best plan to pursue; namely, an engagement which is neither too short nor too long, but just sufficient to make a broad and easy stepping-stone between the old life and the new. The result of a very short engagement depends upon the strength and genuineness of character in the individuals, while the haste with which they have consummated so important a step says but little for their wisdom or prudence. A hasty and ill-advised marriage is a bad beginning in life. A very long engagement, on the contrary, is an eternity of that hope deferred which maketh the heart sick, and it is much harder for the engaged girl than for the engaged young man who is "a laggard in love". She has to wait usually, while he works actively, bringing himself into new relations, obtaining new experiences, and in many ways living a life which she can not share, and which is more than likely to interpose a barrier between their mutual sympathy and confidence, and cause them to drift apart from each other.

(Gems of Deportment and Hints of Etiquette, Martha Louise Rayne, Detroit: Tyler & Co., 1881)

The length of engagements could vary quite widely. An engagement of a year or more in a middle-class (or upper-working-class) context would most likely be the result of the fiancé needing to reach a certain position in his career in order to support his wife - waiting for a promotion in a bank or office, needing to get assigned to a living in the church, etc. When jobs were not an issue, the couple might be waiting for an inheritance, an age of majority, or something similar, and of course in all cases there might be personal reasons (they might have gotten engaged in August and want a summer wedding, for instance). But either way, a month was certainly not considered a long engagement.

The thing that's important to keep in mind is that middle- and upper-class people did not get engaged then as we do now, following a period of very intimate knowledge of each other. (I've written a previous answer here which discusses the way that many working-class couples did cohabitate before or instead of marriage.) Young men and women were generally not allowed to be much alone together until they were engaged, and were expected to figure out if they were temperamentally, intellectually, emotionally, morally, etc. suited to each other and fall in love over that before that point. Etiquette writers and novelists frowned on people marrying based on attraction to beauty or the promise of money, without a full interest in and respect for each others' personalities. After the betrothal, they were allowed to be alone together in parlors and in public places during the day, and to write privately to each other - to find out more personal information and develop a deeper connection. An engagement of a decent number of months allowed time for that deeper connection to be created, and for the two people to make sure that they didn't uncover something that made them incompatible and should end the relationship.

The Knickerbocker put it very pithily in 1863:

The best of all arrangements is an engagement long enough to give the poetry of love its full swing, and not so long as to tire out the long-suffering of the lady's relations.