I'd give them until their baby wing feathers are mostly in myself, but I normally use game birds as my broods these days so I can move them nest and all into a separate broody pen. Most breeds I've had can move really well by the time their wings are in, though. Honestly there are so many...
How tall are the stairs? I've had day-old bantams make it up about four inches and large fowl up to about six inches, but more than that and they tend to struggle. Personally I would separate mama and babies out once they hatch anyway, because you don't want any babies getting separated and...