I am not the parent of a type 1 diabetic, but am a type 1 diabetic myself. I was a child when diagnosed, and know the worry you are feeling, for I saw it in my own mother. I AM a mother, though, and know that getting a 4-year-old to eat an exact amount of food borders on impossible.
I personally find that simple foods are the easiest to deal with when trying to balance food with insulin. By this, I mean things that are separated out so that their carbohydrates can be measured or counted exactly. In my experience, foods like chili are hard to perfectly match with insulin
SGG has covered such important topics, and I agree with the approach.
You mention that your daughter gets 1 unit of insulin before meals. This is interesting to me because now that you're getting a handle on testing & food choices, it seems to me you can work with your endo to learn about carbo counting & matching her meal shot dosages to the carb content in those meals AND her activity levels and BG around the time of the meal. Some endos work with Certified DIabetes Educators or nutritionists/dieticians who specialize in DM.
Two numbers they can help you discover & learn to work with (and they WILL change as your little one stops producing any insulin at all, as her hormones change thru growing, and then adolescence ... etc.): (1) Insulin:Carbohydrate ratio and (2) insulin sensitivity factor. THese numbers often vary by time of day, too.
(1) insulin: carbo ratio -- This is the number of grams of carbos that one unit of insulin will "cover" -- just enough that her BG before and her BG 4-5 hours later is about the same. This number is important to determine how many units of insulin to take for a give meal or large snack. It is used in conjunction with current blood sugar & activity level.
(2) insulin sensitivity -- This is the number of "points" our BG will drop if we take 1 unit of insulin. THis number is important to know when we try correct a high number.
Finally, for folks who take tiny amounts of insulin, there are low-dose syringes (that make it much easier to see and deliver, for example, 1/2 unit increments.) For folks who take really tiny amounts, they also make a diluent to dilute a normal vial of insulin. The reason to dilute U-100 insulin, where 1cc=100 units is to create a U50 or U20 insulin where 1cc has 50 or 20 diluted units. Again, having a diluted insulin can make it easier to measure out 1/4 or 1/2 units at a time. There is considerable training to safely diluting and safely using diluted insulin, but it can be a great tool if your endo wants you work with fractional units.
It may be too soon to consider it, but age 4-5 is not too young for pump therapy, which makes it MUCH easier to dose in tenths of a unit as needed.
Good luck. There's a lot to learn and yet it's clear you've learned a tremendous amount already.