We once went about 8 months without dogs or cats - it was probably like having withdrawal symptoms from smoking or drinking, I guess. Then I 'cracked', got another mutt, then two more moggies, then a second dog - again.
We'd never go that long again, but don't forget that you wouldn't be disrespecting the memory of one which just passed away by getting another soon after - you'd be giving the next one the loving home your last one had. Well, that's how I look at it, there are always loads of them looking for a good home.