As with today, there were many different terms used in medieval times and what a little girl would have said would have depended very much on her upbringing / social background and perhaps the immediate environment in which she found herself.
She could just use the verb piss as it was not considered vulgar until circa. 1760. Here are a few possibilities (nouns) where she could go (this is one verb used with at least some of the nouns below):
- go to siege, presumably related to the French siege, meaning 'seat', and probably used by those of high social standing such as knights. The use of siege is also mentioned in Christopher Coredon & Ann Williams, A Dictionary of Medieval Terms and Phrases).
- privy, as in "it would be more decent to go to the common privies of the city", from an incident in 1307 when a king's groom was confronted by two Londoners for urinating on a side street. The Dominican monk Felix Faber of Ulm, writing about his travels as a pilgrim between 1480 and 1483, advises fellow pilgrims to "go to the privies three or four times every day" (cited in The Porcelain God: A Social History of the Toilet by Julie L. Horan). John Lydgate, in Pilgrimage of the Life of Man (translated from the French c.1475), mentions "goyng to pryvee".
- she might ask for a chambre coi (chamber pot) (OFr. coi < L quietus = quiet, at rest). Chamber pots were also known as originals, jerrys and pisse-pots.
Medieval Chamber Pot (1300-1500), Yorkshire Museum collection
- easement room or chamber of easement, a euphemism of the time.
- longaigne (in a castle), "usually opening directly into a ditch
below...being always open to the outside, they were a weak point of
defence during a siege"
- rere-dorter, meaning literally 'at the rear of the dormitory' in, for example, a monastery. It was sometimes referred to as necessarium (the necessary).
- necessary house. One such was built by Henry I's wife Matilda; it emptied into the Thames.
- garderobe, "small room for keeping robes and clothing. Later, it was used euphemistically of a privy or latrine; these were sometimes built into a thick wall, directly above a moat."
- pissyngholes, a colloquialism cited with reference to toilets in York over the Ouse bridge.
- gong-hus "Lit. ‘going-house’". The use of the words gong and gang date back to at least the high middle ages with one meaning being go (verb) and a going (noun). Chaucer mentions a commune gong in the Canterbury Tales.
Unless Shakespeare (writing in the early modern period) used an anachronism, water was used in the middle ages to refer to urine; this appears in his play Henry IV (d. 1413). Jonathan Swift (1667 - 1745) is cited by Samuel Johnson, "Go to bed, after you have made water", but I can't confirm if this was used in medieval times.