A toddler's range should be the same as an adult's 'normal' range. These numbers vary slightly, depending on which doctor you talk to, somewhere between about 70-126 as fasting normal (although some doctors say 70 is considered too low), and somewhere up to about 150 for after meals (although some 'normal' people seem to occasionally have tests after meals that briefly rise above that level before their pancreas' insulin production catches up). But each person is different, and the true test for how good a person's pancreas is doing to control glucose levels is not the one-time random test, but the a1c test, done in labs to find out what the 'average' blood glucose levels have been for the past 3 months.
All that being said, your toddler's first tests do look high. Are you absolutely sure that her little hands were absolutely clean? Toddlers do eat with fingers a lot, and if some residue of juice or fruit or some carb-heavy foods that she ate last night were still on her hands, this may cause a false number. Her level 2 hours later was very normal, assuming that she had breakfast in the meantime.
If you test her again in the morning before breakfast, make sure that her fingers are absolutely clean. No lotions containing honey or other sweet-smelling substances that may contain carbohydrates, either.
Some people do have what is called a 'dawn syndrome' whereby their bodies remove all insulin right after they first get up, causing glucose levels to temporarily rise too high. So in these people, their fasting glucose levels can be high, although for the rest of the day their bodies function just fine. This is an issue for both diabetics and non-diabetics, and some notice it more than others. You can do a Google search on the term to find out more about what causes it. It isn't anything to worry about. I just mention it because your little daughter may be one of those people whose dawn syndrome brings her sugar levels up in the mornings briefly.
But the real answer is that, when in doubt, have your doctor run some tests. An a1c would be the best test to see if her pancreas is behaving normally. If you see any signs of the typical diabetes symptoms of extreme thirst, fatigue, excess urination, weight loss, etc., then do rush to get her tested. Moms tend to have an amazingly good 'gut' feeling about their kids' health.