Here is my take on Genesis 1 and 2 for what it is worth. First of all the bible, as best we know, was written without chapters and verses. So originally there was no division between Genesis 1:31 and Genesis 2:1. Genesis 1 and 2 was simply the authors account of creation and not two separate accounts. Secondly, as I understand it, biblical Hebrew had no tenses in their written language such as past, present and future tenses. This had to be determined by the context and or the style of writing at the time it was written. (http://www.jewsforjesus.org/answers/prophecy/hebrew-tenses
Thirdly, although possible, it is unlikely that the author would contradict himself in such a short space of writing.
Here is how I think we should understand Genesis 1 and 2. Genesis 1 is a generalized account of creation. There are no details about how God went about creating. Just a simple statement that God created such and such on this day or that day. This includes the creation of Adam and Eve. Genesis 2 starts with the conclusion of creation week by God resting on the seventh day. By verse 5 of Genesis 2, the author picks up the creation account at the beginning of day three, in Genesis 1, where God causes the dry land to appear and just before the creation of vegetation. In verse 7 of Genesis 2, the author leaps ahead to day six when God creates man. Here, we learn the details of Adam's creation being formed from the dust of the ground and God bringing him to life. The author then regresses to day 3 again where we learn of the creation of the Garden of Eden. It only makes sense to build the corral before we buy the horse to put in it. Back to day six, after man is created he is placed in the garden. In verse 18 of Genesis 2, still the 6th day of creation, God states his intention to create a helper for Adam. But before he does that, he brings the animals that he had already created earlier on that day, to Adam. Remember, that biblical Hebrew had no effective way to communicate tense in their language. It had to be determined in part by the context. Verse 19 of Genesis 2 reads in most translations something like this: "And out of the ground the LORD God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them:..."(KJV). From our perspective it would seem that the animals were created after Adam. But many translators recognized the past tense of this verse and added the word "had" before the word “formed” to keep the account in context and to impart understanding of the scripture in our language (see the translations: God's Word Translation, Douay-Rheims, New International Version and The Darby Translation.). Also, you might refer to the footnote in Bullinger's, "The Companion Bible", on verse 19 of Genesis 2 which refers the reader back to Genesis 1:24 of the original account of the creation of the animals.
The reason that God brought the animals to Adam before creating his helper may be two fold. First, to let Adam name them as stated in the verse and also to let Adam get acquainted with the newly created animals. Remember, Adam himself, was just created. He probably didn’t know his, you know what, from a hole in the ground. Although the animals were cute and cuddly, the closest thing to Adam was a chimpanzee who was rather ugly in the face, didn’t walk upright, had hair all over it and didn’t smell right. God was about to change all that to Adam’s delight. After causing a sleep to come over Adam, God created his helper (still on the 6th day) who Adam called woman because she was made from him. Here was a creature that looked like him, yet different. She walked upright, didn’t have hair all over her body, smelled delightful, and was very beautiful beyond description. The woman was created from Adam’s rib instead of the dust of the ground because, as stated, Adam was to cleave to his wife and they were to become one flesh. God intended them to be in a close and intimate relationship with the woman being created from Adam’s rib instead of a separate entity from the dust of the ground. “This is now bone of my bones, and flesh of my flesh (Gen. 2:23).
In summary, Genesis 1 is a generalized account of creation. Genesis 2 is the account of creation in more detail, especially on day 6 of creation. The scriptures as originally written had no chapter or verse divisions which sometimes create misunderstanding. Biblical Hebrew does not convey tense effectively. Lastly, it would seem unlikely for the author to contradict himself so soon after generalizing the creation account.