I've been to weddings that were as high as 50k and weddings that ending up being a few hundred bucks (including the ring). I've got to say, the less people have spent, the happier their wedding day was and the happier their marriage has been. There will always be exceptions to the rule, but I've never seen the need to spend so much money on one day. The more you spend, the more likely you are to be more stressed. The more stressed you are, the more you drink on that one day. The more you drink that day, the less chance you have on actually having sex on your wedding day (not that you haven't had sex before that, but that's not the point) A marriage is about love and compromise, and by letting your girlfriend dictate how much a wedding should cost, or how big it should be without your input, then you're off to a bad start.
Talk to her. Try to find a middle ground. Maybe you can get her a 1 carat ring with slightly lower quality (still unnoticable to the untrained eye) for less that 3k. I don't think spending 5k on a trip to Europe is too bad, but you'll have to work on bringing the cost down of the actual wedding. You probably will end up regretting it after.