More English!!!! The direct object always has to be a noun. So "out" won't cut it as a direct object. That's why "head out" is a "phrasal verb." I get it. the whole phrase functions together as the verb, and there's no object. (No noun.) Hence we have an intransitive phrasal verb, "head out." I feel well-rewarded for obsessing over this all day.
I'll gladly be your grammar cop, here. "Head," used in that way, is a transitive verb. It has a direct object. You can head out or head west or head into a problem or adventure. We give a lot of our body parts a bunch of poetic meanings. Heart, leg, foot, stomach or backbone all make perfect sense metaphorically, right?
Folks, you'll be pleased to know that "head" used in this way is an intransitive phrasal verb and "out" is just a garden variety preposition. Copilot (Thanks, Satya Nadella) says that the phrase makes sense without the modifier "out." I call BS on that part. Nobody says "Well, OK. I'm gonna head." Say, what? Nevertheless, I'll go with "intransitive phrasal verb," because it sounds like serious English stuff, right?
Wait a sec. I'm second-guessing my grammar lecture. If you're Abby Wambach and you head a volleyball, then it's a transitive verb. The ball is the direct object. But if you head out, now I'm thinking "out" is just an adverb. A modifier-- not a direct object. It doesn't really make sense to "head," in this sense, without a direction, but I don't think the direction is the object. Bottom line, I'm not as smart as I thought I was. If we have English snobs here, please help us out. Meanwhile, I'll see if Copilot or Chat GPT have something to offer. Stay tuned. (I don't think "tuned" is a direct object. You can "stay" without an object, but I don't recommend it. Hahaha)