Six weeks out is the right point to confirm the basics are either already in place or booked. Check your pet's microchip is ISO-compliant and already implanted; if it isn't, this has to happen before the rabies vaccination, not after, or the vaccination won't count toward the EU travel requirements MAPA sets out.
If your pet's rabies vaccination needs renewing, or has never been given, book it now — a first vaccination only becomes valid for travel 21 days later, and six weeks gives comfortable margin if the appointment slips or a booster is needed first. If you're an EU resident without a pet passport yet, this is also the point to book the appointment to have one issued.
If your dog is a breed or type that might fall under Spain's PPP system, start the municipal licence process now. It requires physical and psychological aptitude certificates, a clean relevant record, and civil liability insurance of at least €120,000 — all of which take real lead time to arrange, and this is the step most likely to be underestimated.