I am not up-to-date on everything about your Pip, but I think you might like to look up in the book I pasted below. There may be some clues in the chapter on urinogenital diseases that will help you when you take her into the vet’s.

books.google.com/books

click ‘contents’ and scroll down to urinogenital. It should be active to view.

This is from the same textbook Petzy has linked.

1.6.2 Water metabolism
Rabbits normally drink 50–100 ml/kg/24 h (Brewer and Cruise, 1994) although this quantity is affected by the water content and
composition of the diet. The complex digestive processes of the rabbit require water to be continually absorbed and secreted along
the gastrointestinal tract. Saliva is continuously secreted into the mouth and water is secreted into the stomach. In the caecum,water is absorbed from the contents, which contain 20–25% dry matter (Fekete, 1989). In the colon, absorption or secretion of water varies in each section of the colon and depends on whether hard or soft faeces are
being formed. During the soft faeces phase, caecal contents pass through the colon with relatively little change in composition. During the hard faeces phase water is secreted into the proximal colon and mixed with intestinal contents. The water content of the digesta is highest immediately before the fusus coli and decreases sharply during the passage through the fusus and along the distal colon (Snipes et al., 1982). The complex exchange of water across the intestinal wall permits changes in hydration status without obvious fluid loss.
The rabbit kidney differs from other mammalian species. In common with neonates and amphibians, there is a wide variation in the number of glomeruli that are active at any one time. Hydration, uncomplicated by vasoconstriction, leads to a marked
increase in glomerular activity. As much as a 16-fold increase in water diuresis is possible without significant change in glomerular
filtration rate. When blood pressure is increased, there is little or no change in renal plasma flow (Brewer and Cruise, 1994).
…….
Rabbits normally drink 50–100 ml/kg/24 h (Brewer and Cruise, 1994). The composition and water content of the diet affects this quantity. Rabbits that eat fresh greens may not drink at all (Cheeke, 1987). High protein diets require a high water intake. Fibrous, dry foods absorb water in the intestinal tract and therefore increase thirst. During periods of water deprivation, food intake is reduced,
sometimes to the point of anorexia. Conversely, food deprivation results in an increase in thirst with rabbits drinking up to 650% more water (Brewer and Cruise, 1994). Some rabbits never learn to use automatic drinkers and will only drink out of a bowl. Water deprivation eventually leads to dehydration and prerenal azotaemia.

A bit “wordy” but hope it helps understand some regarding their water intake.

To keep Pip cool (and other bunnies) a 2-litre bottle can be filled with water and frozen. Lie it on its side where Pip can lie next to it. You may already have heard about this.

Jerseygirl, you come up with some very informative things. Though the terminology in the article you posted is somewhat scientific for the lay person, it is very informative. With you – and my bunny – I learn something new everyday. Thanks!