In a perfect world
This is such an important day for your family, and you want your new baby to be a part of the memorial service. No one will mind a little bit of fussing.
While some think that the presence of young children at a funeral isn't appropriate, most people take their baby because they have no choice. Often, there isn't enough time to arrange for childcare; plus, many of your usual babysitters (grandparents, aunts, uncles) will probably be at the service too. Your relatives aren't likely to be offended if your baby acts up during the eulogy, but it's a good idea to sit near the exit so you can step out if necessary. If the deceased was not a close relation or good friend, make sure you talk with the immediate family before bringing your baby.
Pay your respects.