Space Heater

I have often heard horror stories about different types of space heaters and I vowed never to get one. Now though with the addition of our new baby, I see that there is a reason we should invest in some sort of heater that we can move to different areas of the house when she is colder than we are. Recently I was reading about ventless gas fireplaces and I wonder if this would do the trick? Are they cumbersome? I have read that they are easily movable and you can have heat in any room of the house within minutes. Would this be comparable to a space heater?