Hi, our son is similar, walks just fine but has no sense of danger. 99% of the time he is fine but he can be unpredictable and randomly try to dart out into the road, so we have to watch like a hawk. Our DLA is mid tier for care and low tier for mobility, he doesn't need pushchair or support like that so doesn't get into the higher tiers.
Have you looked into whether you qualify for carers allowance in addition? Because of the amount of care our son needs, it hinders the ability of both me and my wife to work full time. Currently my wife supplies a lot of the care (he is at school but off term care is really difficult esp Summer, we have very little family support) and is struggling to get any job that fits. You're prob already aware but if not worth a look. Hope this helps.