Is it permissible for me to propose to the girl I love and rely on Allah, or should I wait until I find a job, knowing that I suffer from strong sexual urges and do not want to lose this girl?

If you are in urgent need of marriage and are capable of it, then hasten to it and rely on Allah. Inability to provide financially is not an impediment, for the Prophet, peace and blessings be upon him, married off those who possessed nothing but an iron ring, and those who possessed nothing but an izar (waistcloth). Until marriage becomes easy, be patient and practice chastity by fasting, lowering your gaze, staying away from provocations, strengthening your connection with Allah, and supplicating.