Hi Honey and congratulations that you made it till 6mo:)!!!
So, let's get started:). It's great that you already get rid of a dummy. It can be a real struggle to constantly pop it back, I know it! With DS1 during 12wo wonder weeks we also resorted to dummy and it ended up so badly that I get rid of it around 14/15wo. And well done for not nursing to sleep. The problem you now have is that you change one prop to another one which is holding to sleep or rocking - which can have the same impact as dummy or nursing to sleep. At 6mo she is definitely ready to start self soothing in her crib for naps and nights which should significantly improve her nights and maybe go for better naps.
From my experience, the best method is shhh/pat in a crib without even much of pupd (only if the crying goes for long spell) as many kiddos get stimulated by pupd. So no matter how long it lasts and how hard it is - you have to preserve, be close to her, with your arms, voice but concentrate on settling in a crib.
Don't worry much of short naps. When you are after sleep training and they are still short you will tweak your routine and hopefully get good naps. Firstly start from the basics so from her skill to settle by herself. Short naps doesn't impact night as such, but being overtired can do it. So when you day consist from only short naps, that's fine - just do more of then than 2 long:). You may use a source called babysleepsite to look for a good routine with short naps for a 6mo. I like it as they do not pressure on longer naps and advise how to build day on shorter naps than 1.5h.
Hope that helps. If you have any further questions, please let us know:)!