Typically some part of a newel post extends down through the tread in order to give it the rigidity it needs. In older houses you would see the bottom of the newel poking through into the basement. You may find yourself removing the tread anyway. As far as covering, you'll have to lay it out using manufacturer's dimensions for the new newel.

Kelly:

This is not a DIY project unless you have experience as a boat builder. Don't start unless you are positive you can finish. You do not want to be in the position of trying to hire a stair builder to bail you out. That's gonna sting. A lot.

You have an over the post railing system which won't be compatible with a newel designed for a post to post railing. The scope of work required to convert all that will make the cost of replacing the starter step tread negligible.

That said, a handful of 3/4" oak plugs will fill the holes left by the spindles.

Everything is doable but you will need to contact a stair and railing company that has experienced railing installers or an experienced carpenter who works with railing installations. As Joe mentioned it will cost a little.

Kelly:

I've done some stair building and hand railing. I quit quoting the work a decade ago after not getting several jobs in a row. I won't lower my standards and the marketplace obviously won't pay for them.