Can't believe you live in the same road as me.
No not a silly questions at all I did wonder when I first went what I would have to do. Luckily no you don't have to run around (especially in my current condition). There is a group time thing at the start and the end normally a song with a few silly moves (my son hates that bit just wants to go and play). Then in the middle the whole gym is set up with lots of toys, climbing frames, trampolines etc. There is no structure they very relaxed and can just go on whatever they want. They normally have a theme each term, and change the equipment around each week a bit to make it different. there are lots of Mum's like you who also have a small baby who often but them in a sling or leave them in their pram if having a sleep.
Here is the website:- Classes - Tea Tree Gully Gymsports, Womens Artistic Gymnastics, General Gym, Trampolining, Cheerleading, Kindergym
Would love to meet up for a play date, will send you a PM in a bit, so we can arrange a day.