The context is that Lucy is “’ollerin’ and carryin’ on” (that is, crying) because she is unhappy at the prospect of killing the rabbit:
Lucy began to cry. She had not lived all her life on a farm for nothing and she knew very well that everything her father had said was right. But she was upset by the idea of killing the rabbit in cold blood.
Richard Adams (1972). Watership Down, chapter 48. Penguin.
The meaning must therefore be:
John Downes (1986). A Dictionary of Devon Dialect, p. 26. Padstow: Tabb House.
Lucy must be younger than eleven years old, as her father muses that she “was very likely goin’ to grammar school”, so it seems unlikely that he would compare her behaviour to drunkenness, as suggested in the other answer.
A note on “’ollering” since this seems to be a difficulty. The OED says “holler, v. 1. cry out loud” and although this is usually “cry” in the sense “shout”, it can also be “cry” in the sense “weep and wail”. Two citations for this sense:
A man with a baby in his arms wearily drifts to the coffee-stall, waiting for the belated all-night train. And at once this company of nightbirds and homeless populace become absorbed in one overwhelming problem—how to stop the baby crying. […] A “certain old drab,” half-starved, is stuffed with coffee and sardines and promised “tuppence” to stop the child's “’ollering.” She immediately succeeds.
Charles Masterman (1909). The Condition of England, p. 204. London: Methuen.
And when grandfather went down and teened† a candle and oped the door, there was two voices, if you please; for Christian was talking and a babby was screaming! [… Christian said,] “To the stone I went, brave as a regiment of soldiers, but scarce was I beside it when I heard a child hollering and shrieking like a sucking pig being killed.”
Eden Phillpotts (1921). Told at ‘The Plume’, p. 205. London: Hurst & Blackett.
† teen, v. To light, kindle (Joseph Wright (1898), English Dialect Dictionary, volume VI, pp. 54 & 153.)