People on the internet have noticed the same thing you have, and have come to the same conclusion.
But beyond that, there's little to go on (at least for the manga):
JNat's answer says Amestris was inspired by England, pointing to the FMA wiki.
There's a more nuanced explanation on another page of the wiki:
Arakawa has stated she didn't use any specific countries or cultures to create Amestris, but rather a combination of several European countries from several different periods between the 17th and 19th centuries and, more specifically, the changes that occurred in the Western Europe during the Industrial Revolution (with a greater inspiration in England). According to her, however, there's no implied relation or comparison to any specific country, time, or government.
Do note that the wiki cites no source for either of these quotes from Arakawa (this one and the one cited by JNat).
In this continuity, the Elrics' world is an alternate history of our own world (Christianity is mentioned as a dead religion), so regions of our world correspond with regions of theirs -- and here, Amestris is the parallel-world counterpart of Germany. We know this because
in Conqueror of Shamballa, we see that the parallel-world counterparts of several characters (Edward, Alphonse, King Bradley, Lust, Scar, Hughes and his wife) are residents of Germany.
While Amestris is roughly the correct shape to be the Weimar Republic, the rest of the continent is out of shape. Drachma, which seems to be basically Russia, is along the wrong part of the boarder to Amestris to be Russia. Also, there is no massive desert east of Germany. Also, Xing, the country past the desert, has the culture of feudal Japan but is closer to the size of China. So no, the geography (at least politically) doesn't match up. Also, Conqueror of Shambala isn't cannon to the manga, and it's the manga that counts when it comes to what is or is not part of the universe.