How do I tell my girlfriend that her slightly deep voice is sexy and doesn't sound like a dude's at all without her getting embarrassed?

I might suggest you say the first part and leave out the second part.
Just tell her it sounds sexy...... Omit the dude part.
As far as embarrassing her..... Well if you are doing it in private..... WHY would she be embarrassed

Start with smile and really hard while she talks so she ll say what and you tell her I love your voice and tell her y and when your done explain and tell her that its the cutest to you or something along that line...then tell her keep talking.