My son was 18 months at diagnosis, and we managed with shots for the first 10 months. It *was* a rollercoaster. In part, our trouble was that we were using Humalog (rapid-acting insulin) diluted with saline because the amounts he needed were so tiny, we couldn't measure them with the syringe. Unfortunately that meant that there really was no consistency in how much of the dose was insulin and how much was saline! His BGs swung wildly between the mid-300s and the mid-80s. I got almost no sleep that whole first year because I was so scared that he'd drop low overnight, and the response was so very unpredictable. That ended up being the rationale for putting him on the pump once I was able to sort out the insurance situation. I would strongly recommend getting your daughter a pump if you can simply because managing the doses is considerably easier when you have such a small one. It is no walk in the park to start pump therapy, but if you read up on how it's done (Pumping Insulin is the book that is recommended by almost everyone) in the long run using a pump can really, really help stabilize blood sugars. We put my son on a Medtronic Paradigm pump and saw results very, very quickly; he had been consistently above 8% in his HbA1c while on shots and it immediately dropped to 7.4% once he started on the pump. There were a few more ups and downs in the interim, but we haven't been above 8% since he was 3 years old (he's now almost 7 and in his fifth year of pump therapy) and we've kept it consistently below 7.5% since he was 4.
Granted, there are drawbacks. Unlike with a syringe, you can't always be sure the insulin is getting where it needs to go (the cannula can get crimped, bubbles in the line can stop insulin flow, and so forth) but once you know what to watch for and what the warning signs are of stopped flow of insulin, you can fix the problem pretty fast. I would take a crimped site over having to give 6 injections a day any day of the week.
So yeah, as far as my experience is concerned, I'd say you're going through the exact same craziness we did. It *will* get better. Hang in there, you're in the right place.
Also! If you do get a pump, send me a message — I have a template for a pocket that you can sew onto the back of your daughter's clothes so the pump is conveniently located out of the way. It keeps it safe from her explorations and is a great deal less expensive than buying similar clothing, especially since most of the companies that sell such clothes don't make them in sizes for very small kids. (And, the clothes are plain and kind of boring – I like to make pump pockets with bright fabrics that go with standard kid clothes).