Is it permissible for a new Muslim to temporarily continue working as a women's hairdresser until he finds another job?

If you are able to earn a living through permissible means, even by borrowing what you need to survive, then it is not lawful for you to return to this abhorrent job. It is not an act of gratitude for the blessing of Islam to revert to disobedience.

However, if you find no other means and your continued unemployment would lead to your ruin or the ruin of a family member through starvation, or cause you harm, then you are compelled to undertake this work.

Nevertheless, necessity is determined by its extent. As soon as the necessity ceases, it becomes unlawful for you to return to it, in accordance with the Almighty's saying: "But whoever is forced by necessity, neither desiring it nor transgressing its limit, there is no sin upon him. Indeed, Allah is Forgiving and Merciful."