The verb tenses in Hebrew are not the same as ours, so it is sometimes very difficult to translate and interpret with the same thought as the author intended.
The verb tense here is Qal, which is called the imperfect, but could be translated as a "present perfect" as Gen 1 should be (but isn't). From what I can tell, it would be best to interpret this from the context that God wanted to give Adam company, so he forms animals after Adam was created. I don't think the "had formed" in the NIV is the correct translation. My preference is " And The Lord God forms every beast". It could be, "and the Lord God formed every beast". I don't think "the Lord God had formed every beast" is very good.
One problem is the Masorites put the vowel points in and influenced what tense to translate in. This verb could be a completely different tense than Qal. In fact it might even be future from what I can tell. It is confusing because the root may be tsrar "crr instead of ycr".
From context I would think your idea is correct.
In his Exposition of Genesis, H.C. Leupold stated:
Without any emphasis on the sequence of acts the account here records the making of the various creatures and the bringing of them to man. That in reality they had been made prior to the creation of man is so entirely apparent from chapter one as not to require explanation. But the reminder that God had “molded” them makes obvious His power to bring them to man and so is quite appropriately mentioned here. It would not, in our estimation, be wrong to translate yatsar as a pluperfect in this instance: “He had molded.” The insistence of the critics upon a plain past is partly the result of the attempt to make chapters one and two clash at as many points as possible (1942, p. 130, emp. added).
Hebrew scholar Victor Hamilton agreed with Leupold’s assessment of Genesis 2:19 as he also recognized that “it is possible to translate formed as ‘had formed’ ” (1990, p. 176). Keil and Delitzsch stated in the first volume of their highly regarded Old Testament commentary that “our modern style for expressing the same thought [which the Holy Spirit, via Moses, intended to communicate—EL] would be simply this: ‘God brought to Adam the beasts which He had formed’ ” (1996, emp. added). Adding even more credence to this interpretation is the fact that the New International Version (NIV ) renders the verb in verse 19, not as simple past tense, but as a pluperfect: “Now the Lord God had formed out of the ground all the beasts of the field and all the birds of the air” (emp. added). Although Genesis chapters one and two agree even when yatsar is translated simply “formed” (as we will notice in the remainder of this article), it is important to note that the four Hebrew scholars mentioned above and the translators of the NIV , all believe that it could (or should) be rendered “had formed.” And, as Leupold acknowledged, those who deny this possibility do so (at least partly) because of their insistence on making the two chapters disagree.
It seems to me that Gen 1 is clearly a chronology. And althought it has both animals and man listed on the sixth day, Gen 1 does mention animals first.
Gen 2:19, the emphasis is on the fact that God formed each out of the ground. The passage doesn't seem to be concerned with timing in a way that one should assume that the timing conflicts with Gen 1. Instead one should read Gen 2:19 in light of Gen 1.
And while Gen 2:19 is in the context of making a helpmate for man. It's not reasonable to assume that God was making all of these animals for that purpose and they were all failures. Rather, God presents them to Adam for naming and to demonstrate that they are not suitable helpmates prior to making Eve.