"Face up" is an idiom meaning "lying on one's back, as opposed to on one's front". It can also be used for inanimate objects which have a distinct front, but it would not normally be used for anything standing.
"Head up" is an idiom meaning "holding one's head up straight, not hanging down". It does not usually mean "looking upwards", though it could have that meaning.
"Heads up" does not have an idiomatic meaning (apart from the recent derived one of "a warning", which is not relevant here), but I think it could be used for "head up" when talking of several people.
Neither idiom is really appropriate in your daughter's example: "are looking up" would be the normal expression. You could say "faces turned up", which avoids the associations of the idiom, and has the appropriate meaning.