I did the Pennine way N to S as part of JOGLE. I camped most of it. there is dog friendly accommodation but you will have to seek it out. There is no dog friendly accommodation that I am aware of between Edale and Marsden, you will have to try in Glossop and Diggle and even then I am not sure if there is any. There is dog friendly accommodation in Malham, Hawes, Tan Hill, Middleton in Teesdale, Alston. Not that I have ever stayed in the ones in the last two. You might be stuck at the north end too. The only decent place up there is Forest View. If you have a driver you have more options and should be able to find something within a few miles of the Way - it needs a lot of internet searching though and loads of phoning, places don't always say they are dog friendly and many do not mention whether they take dogs or not until you get in touch.
I camped with the exception of two nights when The Missus joined me at Tan Hill and Wensleydale.
Good luck! I have done loads of LDPs with my lad and love it.