Childhood cancer symptoms and diagnosis

Wanted to ask for help on how to progress things in terms of ruling out cancer? My daughter is 8, she’s been vomiting randomly (meaning, she’ll be sick once, with no other indication of illness except a mild low grade fever) for about 4 months and we’ve had about 8 incidents of this so far, she’s had low grade fevers the same amount of time, she’s got diarrhoea constantly, she has bruising, she’s pale, she’s never normally unwell but this all started in January and shows no signs of going away - it’s actually getting worse.

My cousin died from leukaemia aged 19 and I feel that the moment I mentioned this to the GP, they were dismissive. Currently we are back and forth every other day, with absence from school occurring every other day too. 

I said I wanted a referral for a blood test via paediatrics to rule out cancer and the GP rolled her eyes and said it’s likely migraines - my daughter has the odd headache but it’s not extreme enough to cause these symptoms. Why is it so hard to have things ruled out? They have now reluctantly agreed to do a stool sample but if that shows nothing - how do you get them to listen? 

I’m close to paying privately as I’m that worried about her.