The bar is 40px and the image is sized at 20px, so to center it like the other text you'd expect 10px padding above and below.
Currently it's only got 5px padding above, which I think makes it too high up, and leaves a weird 5px gap where you can't click on the logo at the bottom.
However, because the logo is a bit bottom heavy with only the "dl" poking up a bit, I think it looks more centered if you have say 8px padding above and 12px padding below (or 9/11px).
As for the docking blocks, I know it's a popular feature (at least amongst administrators of Moodle sites), and technically impressive, but I actually think it actively harms the usability
of Moodle, and doesn't really make any sense on mobile devices so would love to see it getting phased out entirely. (It's never been turned on our Moodle site for those reasons).
edit: while I'm here, it looks like you're bringing in the whole theme CSS
twice, if you examine most elements in a browser you'll see the same declarations twice, with only occasional minor differences. I think I did this before and it was because I was regenerating the whole CSS for the child theme from the LESS, and forgetting to exclude the near identical CSS from the parent theme.