Is it permissible for me to delay the prayer beyond its prescribed time due to janabah and the inability to perform ghusl, knowing that the sun has risen and I wish to delay the prayer and perform ghusl later?

The majority of scholars are of the view that whoever wakes up in a state of ritual impurity (janabah) and the time for prayer is short, he must perform ghusl (ritual bath) even if the prayer time expires. He is required to hasten in performing ghusl and prayer.