Not peds exactly, but in NICU we draw all of our own labs. Strangely enough, most of our labs are done with a capillary heel stick, much like a finger poke for a blood sugar in adults. We have tiny little microtainers (~0.5 mL), and we squeeze drops of blood out of the baby's heel into the microtainer one drop at a time. We also draw up some heel stick labs into a capillary tube (for instance, to run a point of care cap blood gas). For larger volumes (> 1 mL), nurses either perform a venipucture or an art stick. If kids have arterial
lines (either peripheral or umbilical), we draw off of the line. Conversely, in NICU it isn't common practice to draw off of central venous
lines for labs. In the units where I've worked, NICU nurses would get called all of the time to draw labs on neonates in the ED, since lab never draws from such tiny kids; they'd also get called to other units like ED to start IVs.
I actually wrote a post a while back that mentions the topic