You should do glass on that side ,sooo pretty ,solid ,and would not take up visual space

Hmm. Never considered glass. Not entirely sold on that. Seems like it would look a bit strange, no?

I can't tell how much space there is between the existing balusters, but there is a code requirement. Check your local building codes. Last i heard was 4 inches. That said, a baby is a special situation. For guidance, look to the crib. It's also a very steep stairwell. For safety and aesthetics as well, talk to a pro.

I see a couple of options:
#1 fill in with a rail and baluster to match the existing railing and terminate the top of the rail into the ceiling.
#2 If you can't find the same pattern of railing and balusters as the existing rebuild railings on both sides of the stair
#3 Extend the wall to the ceiling. In this scenario you will need to add a new handrail to the on the right side of the stair.

It would be a good idea to talk to a local contractor/carpenter if you are uncomfortable about doing it yourself, Good luck.

More pictures will help. One from the opposite side at an angle, not straight like this one. One back a bit showing bottom of stairs from other side.

What style is the house?

I hope you are uncomfortable doing this yourself. I recently had two wall mounted handrails replaced by a professional. One went in without a hitch, the other took some creativity.

Home is a center hall colonial. I would hire someone to do the work. Here are some more pics of the area including a pano.

It's beautiful; of course there will be a gate at the top. By the time your baby is big enough to walk the stairs alone, do you really need more railing? Attaching the balusters to the overhead will look very strange. I guess this was built exclusively for right-handed people. I can't see any good retrofit solution, but maybe you'll discover one. Have you thought about contacting the original architect?

What is the vertical height of the wall side from the tread nosing straight up to the top of the wall? And what is the railing height on the other side measured the same way?

About 14 inches. The height of the railing is about 34 inches. I would likely replace that railing if I put a rail on the other side. Would prefer to have something nicer than what's currently there.

Would it narrow down your staircase too much if you mounted the new balusters and railing on the stair treads instead of the framework? As if that side of the stairwell was closed instead of open like it is...?

Thanks. I am trying to visualize something that would look good asymmetrical. So far, nothing. Will chime in again if I get an epiphany :) The only thing that sounds right so far are spindles all the way to the ceiling the entire length on the wall side.

Thanks, Fred. I'm worried that would look like prison bars!

Yes, that is why I started out saying "So far, nothing." :( but everything else seems like a patchwork afterthought.

Would you consider a temporary solution -- something to remain in place until the child is able to navigate the stairs on their own?

Something like a clear plastic and simple white painted wooden framework? Designed to be sturdy, and easily removable with minimal cleanup -- patching and painting.

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Looking to revive this thread. Anyone have pictures that show a similar "half wall" with a railing attached?

I would just demo that half wall and install a railing of your choice into the stairs. Start with some nice newel posts and work your way from there. I think the key is getting rid of the half wall, not building up on it. You want both sides of the staircase to match.