Some things I'm noticing. You need to drill the hole for the badger knot, quite a bit deeper. I can see the base plug, and it needs to be set deeper. Try and leave somewhere around 50mm of hair exposed above the handle. If you glue it in the way it is now, you'll end up with a brush that's a floppy mess and wont make lather from anything.
Your shape and sanding look very good. Beech wood is perishable, which means you need to finish it with something. If you wanted to used something that's quick and easy, Just use a regular Tung oil or linseed oil. Apply a generous amount, then wipe clean after about 15 min. Try and do 3-4 coats. Should be all it needs.