Hi Aaron,
You will need to use the follow me tool (scroll don to the bottom where a cone is made similarly) to model a dome.
Also see attached file for ideas (open it and lick on the scene tabs).
Ah yes, and welome. I used to suffer with my first domes until I found out how easy it is to make one with a couple of clicks 😉
You can also turn on hidden geometry (view menu) to se how your new ome is constructed. You could have, of course, hand stitch your "wireframe" dome from endpoint to endpoint to achieve it and then soften all the lines. Sometime (with lesst regular geometry) that is actually the way we do it.