Not as simple as a 'good make'.
String instruments need to be 'set up' properly... some shops will have you believe that set up means putting the bridge up and tightening the strings... This is rubbish! A good set up fits the bridge properly to the belly of the instrument and ensures that the insrument is easy and responsive to play and it takes a skilled luthier to do this well as there are lots of adjustments to be made to ensure the instrument is easy to play and tune... It is not a task for the saturday staff at your local music store!
Really worth buying / hiring a string instrument from a string dealer not a one size fits all music shop, as a badly set up instrument will be horrible to play and she will be 'fighting' it not working with it.
Many variables to string instruments - a basic model can have a beautiful tone if set up well and if it has some decent strings and a nice bow with it.. Will be nicer to play than a more expensive instrument that is poorly set up.
You may get a bargain off e-bay / internet, but unless you know what you are looking at - you could waste a lot of money...
some 'damage' can be cosmetic and some can be intergal to how the instruments sounds. You need to know what you are buying if you go for a second hand instrument.
Really recommend you take your teachers advice and get an instrument that is the right size and set up for her.
Many string teachers have little instruments you can hire, or can point you in the right direction of a decent string shop. (At 6 you may be looking at a1/10 , 1/8 or a 1/4 size cello, depending on the child's size.) many variables to consider as different makes of instruments will 'come up' differently on a child, so they need to try it and see if it is a good 'fit'.
Sorry if that isn't very helpful - but I really would recommend you take good advice from someone who really knows about strings. - String instruments are hard enough to learn without having to fight the instrument that is badly sized or badly set up.