I wish my toddler would play outside on her own - but she is terrified of being anywhere outside by herself in case a dog should approach her

In the case of the bed though, she decided at 16 months that she no longer wished to sleep in her cot - it just took mummy a week of terrible bed times to realise that my great sleeper had had enough of the baby bed. She went into a foldaway bed until we moved 3 weeks later and I bought her an ensemble. Never had a bed rail and never fallen out except when she was mucking around.