It seems to be peer-reviewed, but that's not really conclusive of the study's quality. The article itself admits in its abstract that it's only looking at correlation, not causation:
In this study, which only allowed for the calculation of unadjusted observational associations
They also used a convenience sample, children that showed up at 3 clinics. And they also admit that:
There are undoubtedly demographic differences within the two groups studied (vaccinated versus unvaccinated), especially regarding socioeconomic status and maternal education.
One of the authors of the paper discloses (in it) that he's on the board of Children's Health Defense, an organization known for campaigning against vaccines, more or less openly; e.g. that wiki page says a WaPo investigation concluded they funded Facebook ads drumming up the risks of vaccines. The other author of the paper in question is affiliated with a more obscure organization, but its name probably speaks for itself: Thinktwice Global Vaccine Institute. As such, this paper is the kind of information you'd expect such groups to focus on...
The journal itself, which has a wiki page shows that it's a relatively new journal, with papers that (insofar) aren't cited often. And it seems to be less selective in the kind of papers it accepted, in that it is a "mega journal", typically
accepting articles for publication based on whether they are technically sound rather than selecting for perceived importance
And from the journal's own suggestion for related papers, it's easy to find a similar (2019) one on the correlation between HPV vaccines and asthma; an author of this other paper, Mark Geier is better known because his older publication have been roundly criticized (for their wrong conclusions and questionable methodology) by some high-profile academic/medical association, e.g. by the Institute of Medicine or the American Academy of Pediatrics.
N.B., as it turns out David Gorski's blog has (much) longer critical piece on the 2020 study.