Nice one, those type of chairs are hard to date because they have been making them for ever. Sometimes you can date them by the ends of the cross-bar spindles as to whether they were hand-made or machine made.
With nails holding the back “slats” in place I will guess made in 30’s or 40’s. And that looks to be a new seat so no value in dating the chair.
Those types of “child chairs” are quite collectible, or use to be. Someone hereon will put a “going” value on it for you as soon as they see your post.