Yes, your fast is completely valid. Aishah and Umm Salamah reported that the Prophet (peace be upon him) would enter the morning in a state of janabah from intercourse with his wives, then he would perform ghusl and continue fasting. This shows that a wet dream during sleep or delaying the ghusl until after Fajr does not affect the fast; one simply performs ghusl and prays. Purity from janabah is a condition for prayer, not for the validity of the fast itself.
Evidence — the daleel
Sahih Muslim 1109 ṢaḥīḥSahih al-Bukhari 1926 Ṣaḥīḥ
On deen2u
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.