What happens if self-harm becomes suicide? It's not an enormous leap, is it?
It's an immense leap, and I'm sorry to say that you are just engaging in scaremongering.
The raw statistics are here, at Appendix 1 on page 28.
Firstly, it's worth noting that suicide is hugely more common amongst boys than girls. As self-harm appears (statistics are hard to come by, but I doubt any will argue this point) to be far more common amongst girls, claiming an association is always going to be tricky.
Secondly, rates of teenage suicide are low. Every one is a tragedy, but it's 60, 36, 31 in 2011, 12, 13. That's a rate of 3.1, 1.9., 1.6 per 100 000 for those years. Converted to percentages, it means 0.003% per year. It means a very large mixed comprehensive school of 2000 pupils might expect of the order of three suicides amongst girls per century, or one every thirty years (these are necessarily vague numbers, as we are talking about huge variability).
Self harm rates are incredibly hard to establish, but let's be conservative and say that 5% of girls might be self-harming in a sustained and systematic way which is evidence of continued distress, rather than occasional experimentation or one-off events.
That would be 5000 per 100 000 self harming, 3 killing themselves, so a ratio of about one suicide per 1600 self-harming.
In fact, the ratio for a school will be higher than that, as suicide is distressingly common amongst young undergraduates and people leaving home for the first time, so the statistics broken down into 15-19 includes a lot of people who aren't at school. In the case of the OP, suicide amongst 12 year olds is extremely rare, in large part because of lack of means: I don't have numbers to hand, but if is significantly less than 1 per 100 000.
Yes, I'm sure you'll say "but it's too many!" and I'd agree. But interventions for "suicide prevention" are hardly risk-free, and parents are (as I'm sure you realise) not all sugar and spice. If you intervene in 1500 girls' lives fearing suicide, when only one of them was at risk, it would be a miracle of global proportions for that intervention to not have side-effects, negative side-effects, for at least one of the 1499 girls who were not going to commit suicide anyway. Screening and prediction is hard.
Children who are self-harming are self-harming, and that is of itself risky behaviour. It is evidence of mental distress, and that should trigger help and support. But suicide? At these sorts of risk ratios, a practitioner would have to be very confident of their ground before they started assuming that a child who was self-harming was a suicide risk.