What is the pH of the "filtered" water ?
Why are you not just using tap water ?
In the natural range of bearded dragons, there are occasional springs (natural and manmade (bores for cattle / sheep) , can be over 100 miles from one seep/ spring or bore to another, very little standing water and flowing water is only a once a decade occurrence in much of their natural range) where the water is quite hard (rich in minerals). Typically between 6.5 and 8.5 (so moderately alkaline if pH > 7).
If you need to adjust your water pH, try to keep it between pH 5.5 and pH 7.5.
Water in this pH range:
• maintains nutrient balance
• prevents scale formation in irrigation equipment
• provides effective chemical disinfection.
Water Hardness is expressed as mg/L of CaCO3 in solution in the water
Soft = less than 50 mg/L of CaCO3
Moderately soft = 50–75 mg/L of CaCO3
Slightly hard = 75–150 mg/L of CaCO3
Hard = 150–300 mg/L of CaCO3
Very hard greater than 300 mg/L of CaCO3
Hard water can affect soil, stock and domestic water use, and pipes and equipment.