Can a fetus be transplanted? Possibly NSFW.

No.

There haven’t yet been successful fetus transplants within the mother’s body (think moving an ectopic pregnancy to the uterus.). I think we’re a ways off from that technology.

No

Nope. Too much plumbing would be required. Think umbilical cord, placenta, amniotic sac. plus all the changes in the mother’s endocrine and immune system.

what would be the point?

^^What would be the point? What if a woman can’t carry to term, but wants her baby?

What if the procedure was easier than IVF?

@JLeslie ah, ok, that makes sense.

Organs hook up in more or less the same exact way to every person, all the time. Transplanting is a complicated process, but the idea is simple – replace the old organ with the new one.
A woman’s body grows a placenta alongside the fetus, so there wouldn’t be anywhere on a regular body to put a fetus. You’d have to transplant the entire setup – placenta, fetus, and probably parts of the uterus. Also, a pregnant woman’s body is a cocktail of hormones. Without those hormones, the baby dies. Even if you got the host on the exact right hormones, it would still attack the new placenta fetus because the DNA wouldn’t match. Immunosuppresents would probably kill the baby.
I’m not a doctor, but it might be theoretically possible if you took identical twins, got one pregnant, and put the other on hormones to give her an hysterical pregnancy so her body was ready to grow the fetus. Then the actual transplant surgery would amount to stitching a giant water balloon into someone.
tl;dr – No, not really.