Yes, you can switch the vanity and toilet. Of course the plumbing will need to be revised. However, it looks like a total overhaul is needed.

Instead of doing that, keep it where it is. Since this is a retro bathroom, keeping the sink would be cool. Just replace the fixtures. You can add more storage space by putting open shelves close to the ceiling, so it still gives the space a roomy feel. For example, you could have decorative storage boxes up there.

For a transitional look, use textured wall paper in a neutral or cool color pastel hue. Also, you could add two mirrors on either side to make up for the lack of one in the middle. Below the mirrors, you could even add thin wall storage typically used for shoes from IKEA instead of the upper storage.

A patterned floor would be the ‘pop’ item in this room, adding character to the room. Be careful to use colors that complement the walls, aren’t too flashy, and go along with your theme.

I would suggest posting a to scale rendering of your current bathroom and proposed new layout.

And the obvious question is what is your budget? Remodeling a bathroom is probably the most expensive room - especially on a square foot basis. While it is possible to save some money using less expensive finishes, even a basic bathroom remodel costs between $15,000 to $20,000.

Your bathroom is unattractive and could probably be made more functional. Moving a toilet adds to the cost of a remodel and without knowing more, I don't see how it improves function or even aesthetics. While I don't have a horror of seeing a toilet, most bathrooms have a toilet somewhat in the background versus what it would seem to be like if moved to the sink where it would be completely facing the door - presumably.

Again, I don't now what your layout or size is but my master bath is a relatively small urban bathroom. The toilet is next to what used to be the tub but is now a walk in shower and so it is somewhat "hidden" behind one of the walls of the shower.

If you have a male who lives in the home and likes to shave it may be difficult to accomplish over the existing sink with no mirror above. Where is the shower/bathtub located?