You can put tiles over it, just sand the laminate first using orbital sander and a rough grained sandpaper. You want to rough-up the surface so the face of it is no longer smooth and has a bit of roughness to it so the thinset can adhere better.

Did you do tile work before? If not you can get a tile company and they can do this for you quickly, being this area is not that big it will not be that expensive.

They also have some self stick products on the market today which are very good and well made... I never used them but I've seen in a few homes and it looked real good. You might want to get some information on that also.

Here is the link a few products that Home Depot sells just as an example, you can probably find other retailers who carry products alike.

Good luck