1 month old baby not sleeping on cot

Hello mummies. May I ask if it’s alright for my 1 month plus old baby sleeps on me every night? Or should I start training her to sleep on her cot? I tried AGAIN last night! She will fuss and cry each time I put her in her own cot after fallen asleep! I’ve also tried putting her when she’s half asleep but failed! Should I continue to let her sleep on me till 3 months or I should start now? I know it’s still 4th trimester but I’m worried that if she’s used to sleeping on me then it will be harder in the future. Any mummies experienced the same thing? I would like you to advice me on this. Thank you in advance