RP is basically right. The key to moving a bathroom is the location of the existing plumbing. And the most important plumbing elements are the drain and vent pipes. Water supply pipes are relatively easy to route into the new fixture locations. Moving the DWV lines is a major chore for two reasons: 1) they are larger diameter lines and are made of material that is more difficult to work with (mainly cast iron); and 2) DWV lines must be laid out with specific attention to drain slopes and venting arrangements.
This being said, your job will be easier if the following conditions are met: 1) the plumbing wall (were the DWV and supply pipes are located) is between the old bathroom and the new one (this way connections are shorter and easier and existing vents are more likely to be within acceptable distances from the new fixture drains); and 2) your old and new bathroom lies over a basement or ample crawlspace so that you can make the proper connections from below.
The good news is that the newer DWV materials (plastic pipe and various hubless connectors to go between plastic and CIP have made the job of remodel DWV joinery much easier than it was 20+ years ago when I was an apprentice.
Even with a relatively “easy” set-up, you are still likely not to succeed if you are an amateur working on an old house. You will almost certainly have to cut into an old hub&spigot DWV system, will need to bore some big holes in the timbers, etc. You might be able to do the job, but you’d have to buy or rent some expensive tools that you are never likely to use again. This could run into $1000 or more, not to mention many hours of your time. It might be easier and more cost-effective to hire an expert.