Hi Oswaldo
I think that nine days is plenty of time, but you should spend more in the south than the north - perhaps 3 or 4 days in the north and 5 or 6 days in the south. As you know a visit to a wine region isn't just about the wines and producers (unless you are on a strictly professional buying or writing/research trip), it's about the whole experience of tasting, eating, shopping (perhaps) sight-seeing (whether for spectacular scenery or historical things) and for taking driving/walking tours etc. So, the split I suggest takes into account the whole experience. The north is somewhat of a desert for good places to stay and eat with a few very noble exceptions depending on your budget and whilst the vineyards in Côte Rôtie and Hermitage (and all the appellations in fact) are spectacular, they can be visited in a fairly short time. In the south, you have so many wonderful places to visit in terms of vineyard areas, producers, scenery, interesting towns and restaurants/hotels that you are spoilt for choice. Also, the south is a little more spread out, whereas the north is in a line, so-to-speak, though distances are further (and more tedious on busy roads) than you might think.
In conjunction with serious wine guides, my travel guides are what you need, but I'm much too shy to say that (and it's against the 'rules') ... one place that both my northern Rhône writer, an unknown passionate wine amateur called John Wheeldon and my southern Rhône writer - Master of Wine (and wine broker, educator, writer ...) Liz Berry agree on is a Restaurant with 3 rooms which is really in-between north and south called
La Beaugravière - make sure you spend a night or two there and indulge in the food and amazing Rhône wine list - I've yet to go down there for the experience, but it's very much on my list.
It will still be winter when you are there - and be warned, a few places may be closed for the traditional February school ski holidays, but vineyard scenery should still be spectacular and it is that for me that is memorable in both areas. Let me know by private message/email etc if you need more specific help as I can't really write it all out here, but these are regions I've personally visited on several occasions - you should have a wonderful time.