Fart:
From Middle English ferten, farten, from Old English *feortan (in feorting (verbal noun)), from Proto-Germanic *fertaną (compare German farzen, furzen, Norwegian fjert), from Proto-Indo-European *perd-, *pérde. Cognate to Welsh rhech, Albanian pjerdh, Russian пердеть (perdetʹ), French péter, Ancient Greek πέρδομαι (perdomai), Sanskrit पर्दते (párdate).
Toot:
Cognate with Dutch 'toeteren' and German 'tuten' The german root goes back to Low German where it is spelt the same.
Basically 'fart' goes all the way back to proto-germanic whereas 'toot' only seems to be traceable back to Low German. Old Low German formed between the 9th and 12 centuries. However proto-germanic goes all the way back to the beginning of the first millennium.
Verdict: Fart came first.