A.T.
You can sleep train her at 6 months - she's too young now.
It sounds like she doesn't like her bassinet. Try the crib - and try a white noise machine to lull her and camoflage any noises like traffic or the dishwasher, etc. My son sleeps much better with the white noise on - my hubby snores like a wounded buffalo. I wish I had white noise! ;)
Is the room dark enough? Too dark? My son was a tough napper at that age too - he slept best in the dang car or stroller as long as it kept moving. I took a lot of LONG, long walks.