Yes, by all means, go for it! As long as you did a decent, accurate job, you will surely be able to find a journal that will be willing to publish a thoroughly executed literature review. However, depending on the quality of the review, there is no guarantee that a selective journal would publish it.
As some of the other answers have indicated, a senior colleague as a coauthor could definitely help improve the quality of such a review. However, if you have the right technique for executing a high-quality review, even as a doctoral student, you could still produce a review that could be valuable to a wide scholarly public and could be published in a journal with a wide readership.
Excuse me for promoting my own work, but I have a working paper that specifically addresses what selective journals are looking for in what they consider a high-quality review: Developing Novel and Relevant Theoretical Contributions with Literature Reviews. In summary:
- A mere summary of what the literature says is rarely appreciated by selective journals.
- What they typically appreciate is reviews that highlight conflicts in the literature and either meaningfully reconcile these conflicts or, for unresolved conflicts, convincingly show why such conflicts are practically important.
- "Conflicts" in this context include practically important issues that the literature has neglected, as long as the review convincingly shows that the issues are truly important.
- If there are no important conflicts in the literature (including important neglected points), then selective journals would most likely not find the review to be interesting enough to publish. When there is no conflict in a story, then the storyline is bland.
Hopefully, my working paper could give you ideas and strategies for finding interesting conflicts and framing your survey as an interesting and important contribution. Without a doubt, having a senior colleague would help to more effectively find valuable insights, but with the right technique, I believe even a doctoral student working alone could raise some valuable points.