This is an academic discussion that, unfortunately, has found its way into the writings of some religious leaders who wish to limit women's leadership or have some other agenda. Some writers have suggested that the dancing led by Miriam was a "rebellion" or "revolt" and that it displayed elements of the worship of the Egyptian Goddess and her son Horus. Those who hold a loose understanding of scriptural inspiration will likely accept this as a possibility. Those who view scripture as more divinely directed, inspired, or preserved will not. The truth, as is so often the case, may rest somewhere in the middle.
The problem is in reading back into an ancient text what is believed by some people today and thinking the same beliefs prevailed then. Divine truth does not change - Human social constructions do and frequently. The perceived limitation of woman are often read into a text by people with an agenda of limitation or restriction. A situation with one individual is then used to blanket all other individuals and limit their participation.
If it is believed that early Hebrews did not have women leaders and prophets, then the evidence that they did serve in religious roles is twisted or ignored. If the current view is that women cannot be in those roles they must have always been excluded.
There is no good, logical, or factual reason to suppose that ancient woman did not fully participate in worship and rituals of the God of Abraham. Indeed a close reading of several portions of Genesis, Exodus, and other early writings show women doing just that. Even into the histories of Samuel, Kings, and the prophetic book of Isaiah reveal the presence of women. Some, just like their male counterparts, are good and some are sinful. They are, however, clearly there. It is only later, as commentators and preachers from a culture of limitation and exclusion began to formalize those views, that women were truly excluded.
Was Miriam a false prophet? The scriptures clearly show that she was used of God, she responded as a prophet, interacted with God as a prophet, and was recognized for that authority with respect. She is later the only woman prophet to be named outside the story that introduced her originally and when so named by Micah it is an honorific coupling her with both Moses and Aaron.
If Moses was the Deliverer ( a type of the Christ-Messiah), Aaron was the First Priest, than most clearly Miriam must assume the role of the First Prophet. Moses demonstrated the beauty of a close relationship with God, Aaron's line became the means to keep the people close to God, and Miriam the first of a long line of prophets who would call to repentance, recall the words of the Lord, and encourage the people to live as a people of the one God.