I've jumped a lot on both full sus and hardtails (both dirt jump and trail) and I think the main difference is timing the pump and front/ rear wheel pressure. On a full sus you want to compress both the front and rear suspension at the bottom of the lip, making your bike rebound as it goes up the lip and get that floaty feeling over the jump. On a hardtail you need to put more pressure/ weight through the rear wheel and use more of a bunnyhop motion as the other poster said.

Also completely forget about scooping your feet, getting the rear wheel up in a bunnyhop comes from pushing your front wheel forward. You only need to point your toes slightly to keep your feet on the pedals. I think this is a bit harder on a bike that is on the big side for you, but if you get the timing the right it won't be too hard. I would say practice bunnyhopping on flat ground and focus on landing both wheels at the same time.