“ And as soon as we had heard these things, our hearts melted, nor did there remain any more spirit in any man because of you, for YHWH your God, he is God in heaven above, and on earth beneath.”
The name of YHWH had become a terror in the ears of the Canaanites, as One God Who acted in both heaven and earth (Deuteronomy 4:39; Deuteronomy 3:24), and thus closer and more personally active and wider ranging than their own gods, One Whose activities could be seen in what He did, defeating other people's gods (heaven above) and taking possession of their land (earth beneath). We must not think of her as having a deep philosophical view of God, She was impressed by facts. Her primitive belief would grow and expand once she united with Israel, but she had the basics.
The wording of her new belief was as found in Deuteronomy 4:39, the wording of which had possibly become attached to the name of YHWH in the news about Him that travelled around, or it may have resulted from translating her similar words in those terms. It was her belief in these facts that had persuaded her to side with Israel. But we must not read into them yet a full blown faith. She was feeling her way to the truth.
Thus the hearts of the Canaanites had melted on hearing about what He was doing, and their spirits had drooped within them (contrast Deuteronomy 1:28). The words of Deuteronomy would be familiar to the writer, who would know them by heart, and are echoed throughout verses 9-11, probably unconsciously, as her words were translated from the Canaanite dialect.