I headed for work as soon as I got up this morning.
この場合、次のような言い方ができますよ。
ーI woke up and went straight to work this morning.
「今朝起きて会社に直行した」
to go straight to work で「会社に直行する」
ーI headed for work as soon as I got up this morning.
「今朝起きてすぐに会社に向かった」
to head for work で「会社に向かう」
ご参考まで!