I think it's a pretty good idea generally because as you say your hours will count towards CPL. Are there a certain number of cross country hours you need to have for the instrument rating though? (correct me if I'm wrong with that). Also, instrument rating straight after doing PPL won't be easy, that's not a lot of experience, but still certainly achievable if you apply yourself. Once you've got it though, pay the weather sufficient respect, as Warren9 said weather will ALWAYS be a factor. Don't be committed to do certain flights in any weather, that's for airlines to deal with. Sure the summer months are ahead as you pointed out which will make things easier, but afternoon thunderstorms aren't the the sort of things you want to be getting in the thick of!
Anyway, have fun and good luck whichever way you go
I think it's a good idea getting your instrument rating sooner than later, as long as you're ready to do it.