At 12 weeks old, she is going to pee alot

It really isn't a good idea to drastically limit their water intake. They usually self regulate,
if there aren't any medical issues. A
general rule of thumb for a normal healthy dog, is approx one ounce of water per lb of body weight. This is a general rule of thumb and may vary depending on weather, activity levels etc.
Have you talked to your vet? gotten his/her opinion??