I actually like having the brass tube show through on my BCA pens.
The Hot Pink Crush is opaque enough that you need do nothing to conceal the brass ...
The Hot Pink Aquapearl, however, has thin threads of clear acrylic bands running through it randomly, and the brass tube inside shows through like floating bands of gold. I like that effect.
Your pink crush may be opaque enough to need nothing .... but if you're concerned, then taking a can of Krylon White and coating the outside of the brass tube will be quite sufficient to your needs. Make sure the paint cures first, before gluing up.
Also .... PRACTICE ON SOMETHING ELSE FIRST ... in fact, do 2 or 3 pens first before you do this one! You WILL want to do a different acrylic blank before you do this one. It's important to you, so please practice so that you have a chance at perfect. I understand that you want your first one to mean something to you and to her, but having nothing worth keeping is just not the right way to go.
Make sure you don't work the blank all the way down to the bushings! (acrylic can be chippy, and you'll get little divots all over) ... instead, stop a few millimeters short of your final dimensions and finish with 80 - 120 grit sandpaper before going for your final polish.
I like to work mine with wet micromesh up to 12,000 grit, and then polish with Meguiar's PlastX on the lathe, and then apply Turtle Wax Hard Shell polish, also on the lathe ...
As you can see, the results are very nice. (Was entered into Summer Extravaganza BPC)