I have done a few searches and didn't really find what I was looking for. My daughter has a draw length of 18" (using the yard stick method).
I would like a bow she can grow with for a few years if possible. So what is a good starting weight for a girl her age?

Thanks

How tall is she?  Active? Can she do a couple of pushups?  

Generally speaking I'd say around 12-15# @ 18" but kids are so different at that age we'll need to know a bit more.

15#@22" works well for a lot of 8 year olds. A 48" bow will last for several years, starting at an 18" draw.

Chuck

My 8 year old grandsons were shooting  16#@22 inches their actual draw was 16 + inches.

If you want it to last a few years I'd suggest a,little longer bow like 52 to 56 inches.

My daughter is 7 (she is big though) and she shoots a bear cub that is 26 at 26 but only pulls about 19-20"

This is a video of my 5 year-old grandson, Isaac, shooting my 15# bow (on my computer, I have to select "open" after I click on the picture to get the video):

 

Call Mike at Maddog archery and he can put you spot on.  Then order the bow from him and you will be very pleased with the results.  My girl shoots a 24# at 25" with about an 18" draw and handles it very well but she has been shooting since she was 6 starting with a lighter bow.
 wish my follow through was this good.

Thanks for the information everyone. 7 lakes My daughter is 4' 5" she is active in dance, and can do a few pushups. She didn't realize this till I just asked her to try a few minutes ago.

Here's one of my grandchildren at age 7 shooting a 20#@24" Bear Little Bear. All of my grandchildren start on this bow and move up to a 30#@28" Browning Spartan at age 10, girls included. He had been shooting for 3 years when this was taken last year.

 

I recently went through the same thing with 8yr old girl.  I ended up, or I should say she ended up with a 20# recurve at 24".  I had a hard time deciding between the 20# and 24#, I'm glad I went with the 20#, it fits her perfectly.  It sure spits the arrows out a lot faster than her old 12# recurve.

For a straight limbed longbow I'd go 54" & around 12 to 15# @ 20".  Less than 15 depending on previous shooting experience.