Pedosexuals commit a crime, at least in the US, I can't say that it is illegal in every country, because I do not know. The concept of adding Pedosexuals to LGBTQ would in this case be the same as adding rapists to the list. Using the underlying fact that both include non-consensual sex. Having sex with someone who is underage is still considered rape, even if a minor gives consent. The idea is that the minor is not able to give consent.
Even if society changes its morals to allow for Pedosexuals. Legally speaking, I cannot foresee it even being a possibility. I can only imagine the US government's disdain against pedophiles considering the active hatred against individuals who are transgender.
What really bothers me is the fact that being transgendered seems to be considered criminal. Transgendered individuals can be cured from a medical perspective. Transitioning is the cure. However, are Pedosexuals curable? This is debatable and I've heard various arguments. The argument that I find intriguing is that of homosexual to non-homosexual "conversion therapy." Conclusively it is said that it does not work, so accepting this as a truth, can a Pedosexual be cured?