I really recommend going to this website catalog.bd.com/bdCat/listProducts.doCustomer (bd.com). There are plenty of lancets there that you could look into. We currently use the BD Microtainer Contact Activated Lancet blue 1.5 x 2.0 mm. You can find these lancets at this link catalog.bd.com/bdCat/viewProduct.doCustomer. These lancets are not specifically made for infants, but my mother uses these lancets for Genavieve, my fourteen month old sister and Erica my ten year old sister, and they work just fine. I have always struggled with blood tests as I am not very fond of needles, but when my clinic introduced us to these lancets I became much better at doing blood tests. The are pretty much painless and it should only take one poke to get enough blood. More than half the time Genavieve doesn't cry at all!
The other lancets we have used that work just as effectively as the BD Microtainer is the BD Genie blue 2.0 x 1.5 mm. You can find these at this link catalog.bd.com/bdCat/viewProduct.doCustomer. In general we've been very satisfied with the lancets we have used from the BD company.
I am honestly not sure how/if you can order these lancets online, because we receive our lancets directly from our clinic. You will have to explore the website to find out. Have you talked to your clinic to see what lancets they recommend or where you could look for new lancets? I would give you more suggestions, but unfortunately these have been the only lancets we have used that actually work. My only advice is to avoid lancets/lancet pens that are typically used for diabetics. They will be relatively painless BUT they will NOT produce nearly enough blood, and you'll probably end up poking her six or seven times. My other advice is try to use lancets with click activation rather than lancets that require a straight stick (not sure if this makes sense). The lancets I used until I was about fourteen were lancets that my mom would almost litertally have to stab me with, and it was very unpleasant haha :).
Please let me know if there is any other way I can help!