My little girl is 11 and has been bowling on a regular basis with me.  A popular website had a good sale going this past weekend so I jumped in and bought her a polyester starter ball, some shoes, and a bag.  I got her an 8 pounder because that is what she uses at the lanes.  I expect her to be able to move up in weight soon, but it was only $30, so it didn't bother me to go a little lighter.  I am very excited because this is a good step to us spending some quality time together doing something we both enjoy.  We will be getting the ball punched up at the local shop this coming Friday.

So here is my question... Should we drill the ball up with a conventional grip, or go ahead and drill it with a finger-tip grip?  My thought is to go ahead and finger-tip it so she can get used to it, so that it won't be much of an adjustment when we get her something to play the oil with.  FWIW, I am very confident that she is going to stick with bowling.  She has shown a good deal of responsibility and diligence for someone her age.  Where she got it from, I don't know, it didn't come from me.

An eleven year old's hand doesn't need the stress of a fingertip grip.  Drill the ball conventional and let her go bowl.  There is nothing to gain using a fingertip grip at this point. 

At that age I'd drill it conventional, too.  Their fingers aren't usually very strong, so using more of the fingers is probably a good idea.  Less stress on young hands that are growing should be a smart thing in the long run.

Most of us who bowl over may years develop arthritis in those fingers, which is from wear and tear over time.  If she wants fingertip after a few years you can always drill one, but give her time to grow and add strength for now.  Hopefully she'll love the game.

I think it has more to do with your daughter anything else. I have two sons, one is 8 and the other is 7.  My 7 year old is not into sports like my 8 year old is.  we bowled in a league together this summer, a non sanction, no money league. my 8 year old, has very good hand-eye coordination, is super athletic, and in all the sports he plays, loves to work at his game. ( both boys participate in golf, soccer, and bowling ). the older boys ball is drilled fingertip , while the younger's is drilled conventional. the older boy bowls two handed on his first ball, and one handed on spares . the youngest boy, likes to just play so I tried to make it as easy on him as possible.  I think it mostly has to do with how your daughter views bowling at this point.  let her show you how competitive she wants to be, and let her make an informed choice .  I did that with my two boys and that's the direction we went. they both love to bowl, I encourage and praise both of them for what they do, and we as a family have a ton of fun.  also, you mentioned the ball weight, and saying that she could probably go up from 8 to 10 pounds means to me that the extra wear and tear others are worried about on her hands should not be a problem, as long as she has some sort of good form.

these are solely my opinions and what I do with my family, so please take them as such.

Good habits and fundamentals are the same regardless of fingertip or conventional. Good knee bend, body positioning, hitting a target.