You can do yourself, but don't underestimate the amount of work and how long it'll take. Do you have another bathroom? If you have it all planned, all the stuff read to go, with no problems you could still be without a sink & shower for 1 week or more (1 day to remove existing suite, 1 or 2 days plumbing, 1 day installing shower tray and tiling, 1 day grouting, 1 day installing shower frame...). I'm still "finishing" mine after 2 months! I'm a first time DIYer, and managed a good job, but I'm an engineer by background and have an understanding wife!
I presume bathroom is on 1st floor with wooden joist floor? Also presume you wish to replace the whole suite? (it will be difficult to do anything about the floor without moving suite). If you want to do it I would rip the floor boards out and replace with new floorboards or 18mm+ WBP screwed to the joists (I know you want laminate, but see threads on tiling on floors for a solid floor). Obviously carefully think about where you want pipes and waste to run, and do the plumbing before fixing the floor. Good luck!