Based on what you are telling us, I do not agree that Naomi needs more basal at this point. She DOES need more data however. I personally won't make a programming change on my son unless I have two clear indications that:
1). It is actually needed as shown by the data.
2). I know exactly which direction I need to go, and how far, and when.
As you can tell, I'm not a big fan of guessing. :)
To properly set basal rate, you need to see how a missed-meal causes the BGs to swing. If you have the basal set properly, during the 4-5 hours after a "missed" meal you'll stay within about 20 points of were you were when you *should* have eaten. If the basal rate is set too high (too much insulin), you'll drop. If the basal rate is set too low (insufficient insulin) you will see a rise. The caveat here is to make sure you don't have any unusual stressors present (an infection, job stress, or that time of the month) and that your starting BG is in or near the target range. If these entry criteria are not met, the test results will lead you down a blind alley and you'll be back to guessing (Ack! Pthooey!). Ideally you validate again a few days to see how your data holds-up.
Unless you are *really* out of whack and forced to instantly adjust something, I find the "lets wait and see if this is good data" ethic saves you a lot of crashing and banging.
For basal programming I like to set things so there is a slight upwards trend in the BG numbers after a few hours. This way if something untoward happens, you don't wind-up with a bad low.
I note that you have a CGM... which is a darned wonderful tool for basal rate programming. If you are like us and wear it only sporadically, make sure you wear it anytime you are playing with night time basal rates and program the alarms to trigger very early so you have time to respond. Dunno about your daughter, but my son becomes hyper-sensitive to basal changes in the 11 PM to 2:30 AM segment, so even the smallest changes can have large effects. The CGM has been a wonderful safety net for us here and eliminates a lot of the midnight nail-biting.
Edit: If you dont already have it, get the book "Pumping Insulin". It will go a long way towards answering the "is it basal or bolus that needs changing" type of questions. :)