I found that William was just the same at your DDs age and I think many more LOs are the same at 6 months.
I also found myself running out of things to do.. but then I relaxed a bit and realised that its perfectly normal and found that Will loved repeating simple things several times in a day, just because he had done something once it didn't matter, he would do them again happily.
You are doing the right thing as far as I am concerned of redirecting your daughter to something else.
Have a range of activities ready.. and keep swapping and changing - it doesnt matter if she has done it once that day.. do it again. I built in all sorts of silly activities including playing with my clothes pegs, playing with dried pasta or peas in a bowl, playing with plastic kitchen utensils, wooden cotton reels, lying on my tummy and pulling faces, dancing to music in my arms, walking around the garden looking at things, going for walks etc etc.. it was tough some days with the swapping and changing but it did get better.
Your DD will build up her ability to concentrate for longer on one toy slowly but to be honest Will is still pretty much the same.. swapping and changing what he's doing except now he can do things more independantly without me. I just set up different kinds of activity in the living room and he plays happily moving between them with me watching him or joining in.