Spanking or popping a child does not prompt them to hit. Why do children bite? Do parents bite them at home? HARDLY. It's natural for children to hit. Spanking or popping ISNT hitting, it's sending a quick message that this behavior is wrong.
Of course she's going to fall down & throw a fit. It's the response she's trying to get from you that prompts her to do that. Best thing I ever did when my 5 children did this--ignore it. They will wail like they're dieing but trust me, they aren't. If you constantly pick her up, love on her and perhaps give her a treat when she does it, she'll throw one of those suckers in the grocery store when she doesn't get the candy she wants---trust me on that one, LOL. I had a friend whose son did that & he just threw himself on the floor and did the same thing. The child promptly got up & never did it again, he was a bit older than your daughter though.
By ignoring her, you take away her 'power' to get you to respond the way she wants you to. Most likely she'll get louder or do like some of mine did & follow you to the room you're in and throw herself on the floor in there, kind of funny but very annoying. I would just calmly pick them up & tell them this is a no-no and if I felt they were old enough to understand time out, that's where we'd go.
Children are precious but they are also manipulators of sorts. When my oldest son was 4 he wanted our friends dessert so he kept winking at her and smiling as if flirting would give him the dessert. We thought it was funny that a 4 year old would know to do that, we sure didn't teach it to him. BTW, he didn't get the dessert.