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What caused the death of the first kitten and how old is it? If there was an illness that caused the first kitten's death or you are unsure, then the first thing to do is get the kitten checked by a vet to make sure it is not behaving the way it is due to the same illness.

If the kitten did not die from an illness or you get the living kitten checked by a vet and get the all clear (or get it treated to complete health) the a second kitten is a great idea. Most cats will readily accept a new playmate especially if they are under a year old. Depending on the age and disposition of the kittens there may be an introductory period, but it shouldn't be long before they are fast friends.

I'm not an expert or anything, but I'd say just give her lots of love and attention, but don't buy a new kitten right away. She might just be mourning. Getting a new kitten could make it worse for her, like her sibling was unimportant and replaceable.

Maybe just give her awhile to be sad, and then do something big like buying a new kitten later on.

But, like I said I'm no expert.

P.S So sorry for your loss :(

A new kitten has it's pros and cons, but i think you should get one. Your kitten might not accept it right away (it may hiss and claw) but give it 3 to 4 days and it will be happy with a new playmate.