Hi Dilwyn, welcome to the forum!
Your daughter's HbA1c is very good, we are currently at 51 with a pump. There are lots of things to consider if you are thinking of switching to a pump. We were lucky and got one only 8 days after diagnosis so I can't really compare very well, but I can certainly tell you what I do and don't like about it!
Pros:
Only one needle every 2-3 days instead of several a day (not counting finger pricks of course)
Flexibility - your child can pretty much eat what they want when they want, you can do as many boluses and corrections as you like, because you only have to push a few buttons and don't have to stick a needle in each time
Doses are much more accurate - food boluses go to the nearest 0.1 unit, and basal doses are even tinier and can be adjusted by the hour so that you get more when you really need it and less when you don't
You can do tricks like temp basals and extended/multiwave boluses which are not possible with pens. Temp basals make dealing with illness and exercise much easier. Extended/multiwave boluses make it easier to deal with foods that are slow to digest, party buffets etc.
I think it makes it easier at school as well, not having to do injections.
Cons:
Takes some time and a lot of hard work to get the hang of it (although once you do you'll never look back)
Have to wear it all the time, although my daughter sees it as her best friend and doesn't complain, I think she'd miss it now
Cannula needles are a bit bigger and nastier than pen ones. We did have a few issues early on but I'm glad to say we did get over them and now daughter makes more fuss on the odd occasion that she needs a pen injection than with cannulas!
If there are any problems with pump or cannula then blood sugars and ketones can shoot up VERY quickly as there is no long acting insulin in the background. However if you are testing regularly you will pick up any problems before they become dangerous and be able to sort them out. E.g. We did cannula change and pump refill just before tea time yesterday, blood sugar was 4.8. Approx 3 hours later after bath daughter said she didn't feel very well so we tested and got 26.5 😱 daughter then decided to tell me that half way through eating her tea she had realised that the tube wasn't connected to the cannula properly so most of the bolus had not gone in 😱 So we hastily reconnected it all, did correction bolus of 4.9 units, 2 hours later she was down to 19.3, about another 3 hours after that 7.7 - phew. I really must remember to keep a closer eye on her when she's plugging her pump in! Have also had a couple of instances of waking up to BG of 25 and ketones of 3 because of tube not reconnected properly after bath time and therefore no basal all night - oops!
If you get a choice of pumps they are all broadly the same, with a few differences. Only the Animas is completely waterproof and can be left on for swimming. The Medtronic and Animas both integrate with CGMs but the Accu Chek doesn't. The Accu Chek does however come with handy test kit which doubles as remote control so you don't have to fish the pump out from under clothes every time you want to do a bolus or change settings. We've got that one, didn't get any choice which I'm actually quite grateful for because I wouldn't have had a clue which one would be best for us! I have to say that I would seriously miss the remote control capability if we changed to another one. But you have to work out what is your top priority!
Hope that helps 🙂