The situation you are describing is a heavy one, and it is understandable why you feel overwhelmed with a three month old at home while facing a new pregnancy.
First of all, establishing the time marker is key here: your wife is one month pregnant, which puts her in the Nutfah stage, well before the 120 day mark of ensoulment.
From a grounded Islamic perspective, the majority of scholars view abortion as generally prohibited because it interferes with a life that Allah has decreed.
However, because the pregnancy is only at one month, there is more room for scholarly discussion compared to later stages. Many scholars, particularly within the Hanafi school and some Shafi'i and Hanbali jurists, allow for termination within the first 40 days if there is a valid reason.
This is where you have to be careful with your intentions. While financial fear is often discouraged as a reason, based on the Quranic warning not to kill children for fear of poverty, the physical and emotional health of the mother are considered valid grounds.
Since your wife just gave birth three or four months ago, her body is still recovering. If a new pregnancy would severely impact her health or her ability to care for the current infant, many scholars would consider this a legitimate pressing need to justify termination before 40 days.
The raw truth is that you cannot terminate just because of a whim. There must be a genuine fear of harm, whether it is the mother's physical health, her mental well-being, or the inability to provide the basic rights of the existing child.
While the text offers leniency in the first month, it is not a free pass. You and your wife should sit down and honestly assess if this is a matter of genuine hardship.
If the hardship is real, the scholarly path for termination at one month exists, but it should be done with a clear conscience.
Allah knows best.