Short Answer: I would wait before getting a another pet. Remember the good times with the pet that has passed on and love the ones you still have. Grieving takes time.
Long Answer: In 2012 we had to euthanize both our pet cats. It's been an incredibly hard year for me emotionally as they got ill in entirely different ways. One was quite young(3) and the other old(14).
On New Year's Eve I had my 14 year old cat euthanized after a long illness(5 months), there was nothing more I could do for him and he was suffering and I was suffering watching him suffer. I cried at least weekly over him during the time he was ill because I knew it was just a matter of time before I would have to make that final vet appointment. The whole situation was heartbreaking for everyone in my family of 5. We all miss him a great deal.
I also have two dogs so we're not pet-less but we don't plan on getting new cats until the fall(Oct/Nov) and then we will get young cats so they can adjust to the dogs more easily.
The last time we lost a pet, when we were a one dog & one cat family we waited a year before we got a new dog. It felt better to grieve for our missing pet and gave us time to heal before getting another pet. We are only waiting a little less time than that this time because I really really miss having a cat in the house and in our house November is birthday month as myself and my two daughters all have birthdays that month. The two new kittens will be a joint birthday gift to the three of us. Although I will be the one taking care of them - of course.
I feel waiting is better and shows respect for the feelings you have for the pet that has passed. Give yourself some time and space to remember and heal so that if you decide to get another pet you can love them for them and not as a replacement for the lost pet.