For your 4 month old to sleep peacefully in other places not just her cot, she really needs to practice this. Lots of parents ask me this question and really want a baby that is flexible enough to sleep anywhere. So the more often she gets the opportunity to sleep in different places the better. It is certainly a good idea to have some simple, portable sleeping cues. She will already have learnt cues by now. Sleeping cues are really any routine or pattern that occurs when she goes to sleep. Her brain then thinks that she can only sleep when a, b, and c are happening. My suggestion is to make sure the cues you’re a using knowingly and unknowingly are independent of you and portable. For example Independent would be things like, full tummy, wrapped, darken light and radio. Dependent cues would be her own cot, patting, cuddling, rocking, etc.
So first check out what cues your baby has and change any that are dependent or mean you have to do ‘something’ to get her to sleep. At the same time introduce any of the independent cues and you can take those cues with you anywhere whether you are going shopping or away for the weekend. You can take a wrap with you anywhere and this will become the sleeping cue.
Next ensure she has a pattern or routine to her sleep times and be aware of her signs of tiredness so that you find the right amount of awake time for her. When out and about, be sure to put her down for her sleep a little earlier than usual, as she will need longer to wind down. These are just some ideas to help with the transition from cot to other places.