My 10-year-old daughter Grace has strong eyebrows and hazel eyes that turn topaz in sunlight. She has a freckle on her thumb. She also has Asperger's syndrome.

I knew for a long time that my daughter was somehow separate. Not just different, but also … apart. She was eight when we got the diagnosis that placed her on the autism spectrum, and I was shattered. I felt like the world's worst parent for not realising sooner. I felt disloyal, as though somehow I had not truly seen her.

At the time we got the diagnosis, Grace was struggling. Though she is articulate and gifted in art, music and drama, she lacks the ability to read and respond to social situations that come to the rest of us without thinking. She struggles with abstract concepts, and conceptual shades of grey. There's what she's interested in – a colourful but small selection of topics – and there's what the rest of the world is doing.

These characteristics do not make for an easy time at school. At first her peers accepted her eccentricities; very small children tend to take people as they are. But as she grew, her weak points caught the merciless scrutiny of bullies. Grace spent her days being tormented, and being sent out of class when she rose to the bait of classmates who were fascinated by her weirdness and potential for combustion. Maths was a foreign language, and comprehension exercises in English lessons poured poison into the pool of her previously peaceful reading.

I was at a loss to help her. Each evening, I would try to calm her, reason with her, explain how to be around people and negotiate homework that took hours. We had the same conversations every day. She stormed around and sobbed: I shouted. The guilt and sadness grew until they started to blot out the light. I would wake tearful and depressed. My job as a news editor started to unravel and I was prescribed antidepressants. My counsellor asked me what I was going to do about the unhappiness that was clinging to me.

One day, I woke and realised I hadn't done any exercise for months. I hunted for my sports kit – crumpled, musty and a size too small – and put it on, gritting my teeth at the tight fabric on my wobbly thighs. I ran down the road and started to feel ill after 200 metres. After five minutes I wanted to throw myself down in defeat. Running any further seemed an impossible target; something that only other people did.

But then it struck me that Grace, in a strange sense, also had to run every single day. She didn't get to decide to stay on the sofa. She had to battle forward. She had to run up that hill again and again. By setting myself a huge mental and physical challenge, I could show her I was battling too, and make myself strong for both of us.

Within weeks of starting to run, I put my name down for the National Autistic Society's London Marathon team, reasoning that honing my body to endure 26.2 miles would give me the chance to spread awareness of my daughter's condition.

I worked my way up slowly, from three miles, to six, to nine and onwards. In the meantime, I learned more about Grace's condition and set to work finding her the educational and emotional support she needed. I took on the school, the bullies and the local council, attending meeting after meeting, writing letter after letter. I attended support groups and seminars on how to get a statement of educational needs for my daughter. I read everything about Asperger's that I could get my hands on. It was a long, slow process, and there were constant setbacks.

By now I was running three or four times a week, sometimes whooping through the nature reserve before daybreak, overloaded with endorphins and high on being alone to see the clouds turn apricot and lavender with the dawn. Other days it was a weary slog. But it always helped to frame my days, giving me purpose, letting me work off my worries instead of numbing them with pharmaceuticals. There were still times when the emotional overload would hit me and my systems would crash. There were days when I found it so hard to bear my daughter's troubles that I would leak tears for hours. But little by little, my mind and body grew stronger, and the courage and dignity of my daughter inspired me to try harder.

When I think about Sunday 22 April 2012 – marathon day – I remember the noise: the boom and clamour of the crowd all around; the whoosh and thump of my heart behind my ears and in my eyes; the steady one-two-three-four of my breaths, matching my stride; and behind it all a whisper, a murmur behind the din and the pain, a voice that said: "For Grace, my Grace, my girl." She came to watch me, among hordes of thousands, holding her hands out to me over the barriers.

A few months after the marathon, the council confirmed it would fund extra support for my daughter. Grace has welcomed her diagnosis, relieved that she isn't "stupid and useless". She even took the decision to tell her schoolmates about her Asperger's. She is proud of being different and embraces the gifts it brings.

These days my daughter stands tall again and so do I. I am a better mother. There are still tough times. But now I know I can run, and endure.

• Read more on Sophie Walker's blog: courage-is.blogspot.co.uk