Trifle That's very insensitive... I have a couple of friends, one of whom had a miscarriage and another who had an abortion, both at 16, and neither of them saw it as a 'relief that they weren't pregnant anymore', and neither of them had been trying. I had a miscarriage at 18, again, not trying, and it was one of the worst experiences of my life.
It's still a loss and it's still bloody painful, emotionally and physically, whatever age you are when it happens.
OP from personal experience, looking after myself helped. Hot chocolate, crap films and a hot water bottle got me through the immediate first couple of weeks. Don't downplay it because of her age or treat it as a relief - even if that's what you feel, and what she possibly feels, there will more than likely be intense guilt at feeling that way. Keep an eye on her; my feelings of guilt came out in horrendous nightmares and sleep deprivation.
I only started to feel emotionally any better at all after the bleeding stopped - while I was still bleeding, I was still constantly being reminded of it. Wait until a while after the bleeding has stopped and she seems more settled to talk (if you're planning on it) about contraception or the possibility of a 'next time' - right now she needs to deal with what has just happened.
The most important advice is to be there for her. I didn't tell anyone for weeks, by which time I'd tried to 'handle it' myself - and failed. If I'd had people there for me (I was living away at uni and didn't tell any of my friends either), I'd probably have been able to cope much better - as it was, it has and is still massively impacting my life - I got pregnant again within seven months when I'm really not ready, because of various reasons - needing to prove to myself that it was a fluke and wasn't my body's fault, a sense of 'replacing' what I'd lost, etc.
Miscarriage has a deep emotional effect on women of all ages, and I just want you to be aware that even though now she wasn't planning on children soon/showed no interest/maybe even seems relieved, keep an eye on her and make sure she knows you're there if she needs you. She may deal with it remarkably well - it's just best to be on the safe side.