Save your character as a "scene subset", selecting only your character. This will save everything about your character. Works great to save everything as one package.
Another way to do it is to save as a character preset then once your character is saved (usually just the barebones character as you know), then you save what they have on (including hair and genitals) as a "wearable preset", and there are other aspects of your character you may wish to save like their current pose as a preset, just look under FILE->SAVE AS for the various types of presets you can save, in this way, you can save the basic character, then maybe save different wearables for them (different hair and clothes etc), different poses for them etc... without having to load it all in one go with a scene subset.
I often do BOTH, a scene subset with everything, and the separate presets as described as sometimes I don't need it all loaded in.