Current Timeline of Events from 2.0 On

[Seraphor]

a woman you encounter during the questlines goes from pregnant with child but not showing to having given birth to that child.

I think the 'not-showing'-'showing' part is a bit of a stretch, because they simply don't have models for pregnant women. While I'm sure a length of time has passed, I don't think you can gauge how long has passed based on fetus development.

so we're looking at a several months trip both ways by ship.

Do we have a source that states it takes 'several months'? I'd be onboard with 'several weeks', but I think months sounds a bit much. I wouldn't be all that surprised if they claimed it only took a week or two to get to Othard either.

Also baring in mind, during the Stormblood patches with the war wit Garlemald at Ghimlyt. We teleport over to lend our aid, while Doma sends it's troops by sea. These troops do eventually reach the front and join the fight, but we are not told that this fight has been going on for several months. So I'm guessing 'about a week' seems the most sensible.
It may be half-way around the world, but I don't think we can assume the world is just as big as Earth.