My girls all learned their press handstands at home--Coach encouraged them to practice these daily since at that time they were only at the gym 1-2 days per week....I think it is relatively safe, provided that they have an area that has enough space so they will not kick something, and also that they don't overdo it (If they do 100 a day everyday, they can end up with sore wrists).
Which skills are safe to do at home may depend on the level of your gymnast and what skills she has been cleared on at the gym to work on independently--In our home, any skill that requires flight is a no-no: Round-offs, handsprings of any kind, tucks, layouts, aerials are all NO! The reason these are not ok to do at home is partly due to safety..tumbling on unsprung floors can put undue stress on their bodies/bones and lead to sprains/stress fractures. You also don't want them practicing with incorrect technique. Sometimes the skill may look great to the parent even when the gymnast's technique is incorrect. All those repetitions at home may lead to forming bad habits that can be hard to break!
Handstands, cartwheels and walkovers are fine with me, as well as stretching, splits, and presses, as long as they are on a padded surface.