Solitaire game/puzzle-set for a 7-year-old… The company behind Rush Hour
have also made many other such puzzle-sets which you can take a look at.
Kanoodle (not from them) is another such puzzle-set – one that is quite small.
Most cooperative games can be played solitaire, and some games are designed specifically
for it. A few games you can look into are Max* (might be too simple – it’s for 4+), Mmm!,
Forbidden Island (might be too complex – it’s officially for 10+), and Castellion (likewise).
(*It’s the best-known of that publisher’s titles, which are generally children’s co-op games.)