Hi Gabriel,
I believe you can do it with galaxy. I never used it for miRNA analysis because most of the miRNAs of the organism that I work with are not annotated on its genome. You will need the total number of reads that uniquely map to each mature miRNA. What I have notice is that the guide and passenger strand most of the time have huge differences in expression. To get that your annotation file (gtf or gff) would have to have each strand, its okay if you don't have it. Probably you can use HTseq. It is available on the Galaxy tool shed. You can also use it directly at
http://galaxy.nbic.nl/ (it is NGS:RNA Analysis). You can also run it on your computer
http://www-huber.embl.de/users/anders/HTSeq/doc/overview.html
After you get the counts you can use Deseq to calculate differential expression. See if you can get the counts first. I never used the Galaxy Deseq wrapper, but they have it on the tool shed too. You can install R and the Deseq package on your computer. You might install RStudio as well. I can send you the code I used to do my analysis with comments if you decide to give it a try.