It is allowed to study while on TD status; it does not necessarily require a change of status to F-1. However, if your daughter "ages out" (turns 21) she will no longer be eligible for TD status and will need to switch to F-1 status at that point in order to continue studying.
For you and your spouse, there will be no impact on the TN/TD to GC process if your daughter switches to F-1 status.
For your daughter, to apply for F-1 status and to re-enter the US in F-1 status if she should choose to travel outside the US, there is a risk that she will be found not to have "a residence abroad", which would result in the denial of F-1 status. However, many children of foreign workers in the US have switched to F-1 status successfully, even though their parents lived in the US for many years.
I am sorry that I could not provide a more detailed risk assessment because this situation is not often discussed on the forums that I read.