You can ride a moped with learner plates on a provisional license after completing your CBT, but cannot carry a pillion. However, if you want you could opt for a full AM Moped Licence by taking your theory test, followed by the practical test. This will allow you to ride a moped (either scooter or motorcycle style) up to 50cc with a top speed of 45km/h (around 28mph) without L plates, and to carry a pillion.
So, why would it make sense for you to complete the AM Moped License?
The first motorcycle licence practical test available is the AM Moped Licence. This can be taken if you are aged 17 or over. This licence allows you to ride a moped of 50cc or less which has a top speed of 28mph, with a passenger and without learner plates. If you know that you will only ever ride mopeds and have no interest in getting a licence which allows you to ride more powerful motorcycles and scooters, this is the licence for you. If however you want to move through the motorcycle licences and on to more powerful bikes, then it is probably worth missing this step and going for either the A1 or A2 practical test.