Open is essentially PvE - for all practical purposes. Sure, you can find PvP if you go looking, but given the scale of the universe you either have to get "unlucky" to encounter a griefer or player pirate, or careless (e.g. staying around starter systems, known hot spots, CGs etc.). I've played since premium beta and can count on one - maybe two - hands the number of times I've been attacked unprovoked. And, once the basic escape mechanics have been learned, you can escape from virtually any player. Moral of the story: play in Open, but away from hot spots. The folks you/your daughter will meet there are overwhelmingly the helpful and cordial sort.
I must remark to this post. I went again to open yesterday after a long pause (in the other modes and away from the game). I flew for around 1 hour in my DBS before a pilot in Imperial Cutter tried to interdict me (before that I think an Anaconda was trying to get on my six). Absolutely unprovoked as I have made no enemies (not been on Open for a long time and never started a pvp-combat myself) and was non-aligned and non-wanted. But yeah. I would certainly hope for a pve mode where there would be a lot more players to interact with and I could fly all kinds of ships without being forced into these pure pvp configurations before engaging in combat.