I'm sorry but your GP is wrong. If they suspect diabetes they could have done a simple finger prick test while you were there to get things started. There is no way you should wait until next week to get bloods done.
My son is 4.5 and diagnosed with type 1 at 2 and 9 months. He was weeing frequently and I could never get enough water into him to satisfy his thirst. The first GP told me it was a virus and he was drinking so much due to fighting off a fever. She was wrong.
Second GP did the finger prick test as soon as I told her the symptoms. She was on the phone to the hospital immediately. My son was already in DKA.
Please get your son tested straight away. Take him to ED and tell them you suspect diabetes. They can put the numbing cream on to do the blood test. They may want to put in an IV. My son was sedated with gas for this.
I am not trying to scare or worry you but this is not something to muck about with. Kids have died from undiagnosed diabetes.
For what it's worth, once the weeing/drinking started they were pretty much constant rather than on and off.