How hard is it to clean and QC gene expression microarray data?
I am not sure how much you know about bioinformatics already, can you use R? For a bioinformatician looking at QC for microarrays should not be a big deal, at least for me it would take maybe a day (or two) to get this done. However, if you never used R and want to start from scratch, it depends on how quickly you learn how to deal with arrays and QC. There are many tutorials and review papers about normalization and QC of arrays. Try there and see if you can easily understand what these papers are telling you.

Read the limma user's guide, and try to follow the tutorials therein. If you understand that quickly you can try a real experiment of your own. If you don't understand what's described in there, you might want to look for another project for your thesis.