You can convert it to a mutable QueryDict instance by copying it:
request.GET = request.GET.copy()
Afterwards you'll be able to modify the QueryDict:
>>> from django.test.client import RequestFactory
>>> request = RequestFactory().get('/')
>>> request.GET
<QueryDict: {}>
>>> request.GET['foo'] = 'bar'
AttributeError: This QueryDict instance is immutable
>>> request.GET = request.GET.copy()
<QueryDict: {}>
>>> request.GET['foo'] = 'bar'
>>> request.GET
<QueryDict: {'foo': 'bar'}>