If you stain for the protein (assuming you can get the data you want that way), you should easily be able to see it shift from free protein to bound protein.  If you are expecting to see the RNA bands move, if it works at all, the larger RNA molecules will have only a small extra mass from the 10kDa protein, so you may not see much.  (I'm assuming 1 protein:1 RNA -- meaning only a small mass change between RNA vs. RNA-protein complex.)  Also keep in mind that your large RNA molecules will likely fold into many competing structures, which could cause smearing on the gel.  And, lastly, it can be very challenging to keep such long RNA molecules intact, for any experiment -- RNA is inherently unstable (subject to hydrolysis) and any tiny amount of RNase contamination will definitely ruin your experiments. 

With such a tiny protein, if it happens to have a tryptophan, you might have a better time examining binding using fluorescence anisotropy, rather than gel shift.

Criag is right. 

In addition, with most band shifts you label the nucleic acid (either with radioactivity or something like biotin).  This is usually because your RNA can be made pure and you are using a crude mixture of proteins.  For these studies only the lower sizes of RNAs you mention have much chance of showing a shift.  However, if your protein is pure, you can label the RNA with biotin and test for the ability to pull down your protein by capturing the RNA protein with a streptavidin bead and by then eluting the protein from the pulled down complex and running it on a gel.  However, I am also assuming that you are looking for some sort of specificity to the binding.   You will find that if your protein binds to RNA at all it will probably bind to any RNA under isolated conditions.  You will need to set up some sort of competition experiment between your various RNAs and other RNA species to see if there is any specificity.  These kinds of experiments take a lot of care to make sure that you are not looking at non-specific binding

Dear Craig A Gelfand and Prescott Deininger ,

Thank you very much for your responses. Those help me a lot. I'll cut my sequences down to around 200 nucleotides instead. I hope this should work. I forgot to mention both of my protein and RNAs are purified ones. In the active form, the protein stays in hexamer form around 60 Kda. I'll labelled my rna with biotin for Lishtshift chemiluminescent. That case I can switch to a pool down if it is necessary.

Thanks