I've got something to add.....
Canary - my kids started with a one mile fun run that was attached to a 10K I was doing in Liverpool. As they were 6 and 8 at the time (and I thought a mile was quite a long way for a 6 year old) I bought flora margarine to get the free little running bottles they were giving away to celebrate the marathon and said "right - these are YOUR bottles and we're going to train"
I bought them some decent trainers (you'll struggle if her feet are below a size 1) and we plodded on out, at their pace, for about half a mile. One of them would've given Usain Bolt a run for his money and the other one whinged about stitches within 100 yards! But we persevered. I only took them out when they wanted to go, and we got up to a mile fairly quickly. On the day before the race they insisted on pasta for tea (to "carb up")
and we took some jelly babies (for the huge glycogen depletion they would inevitably suffer)
Race day arrived and they treated it like the Olympic 1500m final. I was standing close to the finish line, when, from around the corner came eldest Miss LB (whinger with the stitch) like something out of Chariots of Fire!!!! She was NOT going to be beaten by her little sister! Two seconds behind was youngest Miss LB, busting her lungs out. They did amazingly well and fell over the finish line in tears.
Both Mr LB and I are runners. They've been to the expos and the marathons. They know about preparation and they wanted a go. It's like nicking your mother's make up because you've seen her putting mascara on. What I really wanted to say in telling you all this is that your daughter wants to do it because she's copying YOU and it's a damn sight better than pretending to smoke!
Let her come with you, but find her a little "race" so she can train too. Explain to her when you need to go further that your distances are different, so she can't come on your 10 mile LSR, but you'll train with her tomorrow / Monday /whenever.
Above all make it FUN. Nobody wants a crying 7 year old with shin splints. Keep the distances low.