Chickens are good about doing that kind of stuff, aren't they? Their birdbrain doesn't follow logic quite the same way ours does.
I really would not expect her to follow the eggs. They normally imprint on the spot not the eggs. If you move her I suggest you fix her a cage. It should not be very big. You need enough room for a nest, food, and water. You can give her a bit more, a place for a dust bath would be nice, but don't give her much. A broody hen knows to not poop on her eggs but does not know to not poop in the water or food. You'll be doing some cleaning. That cage or enclosure needs to be so secure she cannot get out and return to her old nest
Make the nest pretty dark, that seems to calm them and help them accept the move. Move her at night with the least amount of commotion and light you can manage. It's best to do this before she gets the eggs she'll hatch as she might not accept the move, but if she is already on the eggs you want you don't have that option.
When I do this (I don't much) I leave the hen locked in that nest itself for most of the next day, letting her out to eat and drink right at day's end. A broody is used to spending most of her time on the nest, this is not cruel. Others go about if differently but this has always worked for me.