The OED, oddly, treats this under definition 7 of peel:
7. intr. N. Amer. slang. To move or drive quickly; to hurry, race. Also (occas.) trans. with it.
1860 J. R. BARTLETT Dict. Americanisms (ed. 3) s.v., To run at full speed. ‘Come, boys; peel it now, or you’ll be late.’ 1953 H. G. FELSEN Street Rod 103 You got off easy… The way you peeled up that street. 1963 in B. L. Chipman Hardening Rock 50 Just tuned my car now, she really peels. 1992 R. ANAYA Albuquerque xx. 239 He smiled and peeled out of the pueblo, leaving a thick trail of dust in his wake.
It seems to me it should be in the “Phrases” section at the end.
(The entry was revised just last month.)