one month old

My baby is one month old and for a while now he just won't settle and sleep through the day in his Moses basket that is downstairs. He sleep fine at night in his cot that is in our bedroom so today I thought I'd try him in his cot for a nap and he fell asleep straight away but I can't stand the idea of him being on his own upstairs whilst I'm downstairs. We have a monitor but I just still don't like the idea. Is it fine to leave them on their own?