The cat was three years old when the puppy came. I didn't do anything to introduce the pup, because I didn't know anything about caring for a dog and also it is my first cat. But I clearly remember that she was out in the yard when I arrived with the puppy she started hissing at it the moment we got in while I was still holding it in my hands. My cat hadn't met any dogs until then - so this lack of socialization does matter.
Well, the dog really is VERY playful (as every gundog) and sometimes just goes to sniff the cat and she starts hissing even if it walks in gently. Probably the cat doesn't want to be disturbed by any "giants with huge noses"

But the problem is that I don't trust them and never leave them alone together.
I don't know - maybe the problem is that my cat is too moody

. She does whatever she wants and nobody can tell her what to do. She is a very spoiled cat - she will do something only if she wants - playing, eating, being petted, etc. For example, if she doesn't want to be petted, she will shake herself and if you don't stop, she will "punish" you by mouthing - it doesn't hurt, it's just a warning.
Though, now our life is FAR more pleasurable than when my dog was young when it chased the cat, I think it can be even nicer. I'm really proud to have trained by myself a gundog from working lines not to chase a cat. That's why I regard training my cat as the next challenge of our life together.
Edit: When I take the dog out in the yard, I always make sure that the cat is inside because she gets very frightened when she sees the dog running.