This is from History of Chinese Literature
(1986) edited by You Guo'en, Wang Qi, Xiao Difei, Ji Zhenhuai, and Fei Zhengang (中國文學史：游囯恩、王起、蕭滌非、季鎭淮、費振剛主編):
Just like "The Peacock flies east and south", "Ballad of Mulan" also raises a question regarding the time period in which it was composed. Views on this issue differ even more than in the case of "The Peacock": every dynast from Wei, Jin, Qi, Liang, Sui, and Tang has been proposed. Some have even hypothesized the author to be Cao Zhi or Wei Yuanfu. At this time, we can be certain that it is a folk song from the Northern Dynasties. Shi Zhi Jiang from the Chen dynasty (557-589) recorded this poem in his "Collection of Songs Past and Present", which is solid proof that the poem cannot have been composed after the Chen. Wars were frequent in the Northern Dynasties, and martial prowess and exploits were greatly praised. This poem directly reflects that social environment. Furthermore, the emperor in the poem is referred to as ke han ("Khan"), and the expedition starts off in the north-- these all support the idea that the poem can only be a product of the Northern Dynasties. It was probably written after the Northern Wei (386-534) moved its capital to Luoyang, and before splitting into the Eastern and Western Wei (534~535). During its transmission, it could have been edited by the literati of the Sui and Tang, leading to its "containing bits of Tang lyricism", such as the six lines from 萬里赴戎機. However, looking at the poem as a whole, we see that it still keeps the characteristic of a Northern Dynasties' folk song.
Liu Dajie's History of the Development of Chinese Literature
(1992) (劉大杰 ：中國文學發展史) also dates "Ballad of Mulan" to the Northern Dynasties:
The time of composition of "Ballad of Mulan" has been discussed since long ago. 後村詩話、藝苑卮言 both contain hypotheses that it was created during the Tang dynasty. Even recent scholars have supported the Tang hypothesis. The reasons they give are the following three:
1. In the Collection of Yuefu Poems, it is written that Wei Yuanfu of the Tang wrote a imitation of the "Ballad of Mulan". The annotations say that "According to the lyrics, there was a song called "Mulan", but none knows when it was written". Later scholars thus hypothesized that the original "Mulan" was also written by Wei Yuanfu.
2. The line 策勲十二轉 refers to the Tang official system, and 明駝 refers to the courier system of the Tang.
3. The four lines following 萬里赴戎機 seems to be the style of the Tang.
In reality, these reasons cannot disprove that "Ballad of Mulan" was a composition of the Northern Dynasties. When we read the original side-by-side with Wei's imitation, we can see that there are definitive differences in the flavour of the two. The original is rich in folk elements: neither of the simple and rustic wordings nor the innocent and lively descriptions can be imitated by a literary person. In comparison, the imitated piece is full of usage of literary conventions and elaborations. We can thus easily tell that the two are written by different authors. Regarding the mention of Tang systems as well as the mixing in of Tang literary style, that is only a sign that the poem was edited and modified by later writers, and not a proof for the Tang authorship hypothesis. The first six lines of the original "Mulan" is almost identical to the six lines in "Song of Breaking a Willow Branch", starting with 敕敕何力力, which is proof that "Ballad of Mulan" came from the peasant class. A writer of later times would never have plagarized it thus.