I think it's more likely that verses 3-4 and 7-9 describe the same event but from different perspectives.
I think this is more of a 'blueprint' of what will first unfold in heaven, and what will later be 'mirrored' on the earth. The way chapter 12 is written appears to be a 'reflected' literary technique called a chiastic structure of writing (we see this style throughout the Bible). The goal of the chapter appears to have two events occurring, one in heaven, and the other from the earth; and the whole chapter meets its main point in the middle which is the result of the war in heaven.
Perspective from heaven:
1. The dragon waits to devour the woman's child (Rev. 12:1-5)
2. The woman flees to a place where she will be taken care of (Rev. 12:6)
3. Michael and his angels overcome the dragon and his angels in heaven (Rev. 12:7-8)
The middle point:
4. The dragon and his angels are cast out of heaven, and heaven celebrates (Rev. 12:9-12)
Perspective from the earth:
1. The dragon pursues the woman. (Rev. 12:13)
2. The woman is taken care of for 1,260 days (Rev. 12:14-16)
3. Enraged, the dragon readies to make war against the rest of her offspring. (Rev. 12:17)
If you ask me, Revelation 12 is an overview of what takes place when the war in heaven begins back when the 'worthy one' on earth is revealed, (Rev. 5:5) through to the moment the seventh trumpet is sounded. (Rev. 11:15) From then on it is the continuation of the dragon preparing to make war against the woman's other children, and the prologue to the dragon standing on the shore ready to bring forth the beast out of the sea. (Rev 13)