Ballpark costs below for plumbing ONLY - no tearout or repair of access points, and does NOT include cost of the basin, faucet, toilet, shower etc - just the plumbing to them with flanges, shutoff valves, etc ready for installation of shower, toilet and sink, etc, plus callback for final hookup of sink and toilet when they are ready.
Depends of course on exact configuration, local labor costs, etc. Assuming in a house (not high rise apartment or condo), typical wood stud walls and wood subfloor and joist construction, and that full tearout will precede the plumbing so walls and floor receiving plumbing will be bare studs and joists, and limited term disabling of existing bathroom use (maybe a day or less a couple of times) while hooking in pipes is allowed - i.e normal job conditions:
Assuming also that the existing sink, toilet and shower are plumbed in the wall that backs up to this new bathroom not the opposite or adjacent walls, and that floor will be readily accessible from below through a downstairs or basement ceiling or crawlspace for sewer pipe installation:
Probably $800-1000 absolute minimum if each component is being tied in directly behind its matching counterpart in the existing bathroom and very easy access, and that all existing piping is copper or plastic rather than steel or iron - easily half again to double that if tying into steel water pipes and ductile or cast iron sewer pipes. Anything other than easiest access could also easily increase that low end to $1000-1500 (modern piping) or $1500-2000 range (steel/iron) - and commonly well into the $2000's if you are having to tie into sewer pipes below a concrete slab.
Bear in mind these are REALLY rough numbers - you need to talk to a plumber, preferably with the wall and flooring opened up in the new room, so he can give you a real price quote - and get 3 bids for this size job unless you already have a plumber you trust from prior experience. Having the work area opened up so he can see what the existing piping runs actually are is critical - could change an hourly-only bid with no cost guarantee or a bid with a lot of built in contingency built into a firm bid that could cut your total cost in half if they can fully see the full extent of the scope of work up front.
One other thing opening it up early on does for you is tell you if you are going to need remedial floor work due to water damge in the flooring, or repair of leaking pipes in the existing bathroom you did not know about and could easily be fixed at the same time.
Bear in mind you may also get a surprise you do not expect - possible floor damage in the existing bathroom that may need repair. Do not make the mistake a lot of people make and assume you can do two bathrooms simulateneously - then almost die when the job goes south for some reason and they find themselves without a bathroom for a month or more. Make sure one gets done before you tackle the other other than necessary piping tie-ins and capping off if the existing bathroom needs to be reworked substantially.
Hopefully Don or Todd or one of the other contractors will jump in here with their thoughts - I am going to guess if they do, they will say I am $500 or more low on my low-end range if anything.