You are welcome to read my farm blog - we got two ponies this year for the kids, and I've had my horse since 2000, moved him to our farm in Feb.
A great start for you would be Equiculture, that I have linked on the farm blog (in my sig), there is also a Facebook page for it. Jane Myers is so, so knowledgeable and going to a seminar facilitated by her gave me so much confidence to move from agisting to keeping my horse with me!
I would recommend some proper riding lessons for your DD and yourself if you've only done trail rides (sorry, you didn't give details on that one!), but for you it's not essential, you can learn later. For your DD it's important for your own peace of mind. You will get reputable word-of-mouth leads for tack, equine services and horse-flesh through your instructors.
My DS's pony is pretty green but she is just a gem - they're already riding down our (albeit quiet) road off-lead, even though she's not been cantered under saddle yet (too wet for me to hop on and do circle and trot-pole work with her yet). DS has been having formal lessons since March and that's helped him so much. It helped that he's been sitting on a moving horse since before age 2, and I've had him on a bareback pad (gives a more natural and stable position than when they rely on stirrups), but all these things can be learned in no time. I picked up riding later in life and my instructor said that it wasn't a disadvantage, it just meant I would learn differently and with appreciation for certain concepts that kids just can't grasp yet.
It's fun, and if you're careful about what you buy it shouldn't be expensive (feed-wise). You just cannot go wrong with an Australian Pony. I got our little buckskin mare from a breeder out in Bendigo, and that's a 3 hour drive for us, but I was on a mission to get the best pony for the money we could spend, even if I had to finish off the training work myself. If you're in Vic, I can send you to two studs to have a look at what they have
I would advise against the classifieds - pleeeeeeeease. Especially if you're new to buying - it's a minefield and will leave you broke! Get to know your land, join your local Landcare group, study the Equiculture materials (great, great stuff on property management that goes beyond horse keeping) and figure out where on your property you'll manage the horses, the feeding, the riding etc. Meanwhile, get the lessons happening, so that when you test-ride ponies you'll have a better idea of what is suitable for your DD's needs.
The upshot:
Lessons
No classifieds
Equiculture
Landcare

Also, check out RIRDC website (govt website) on their publications - some are free, some are downloadable, all are excellent. You may need a Property Identification Code (PIC) for horses (we had one already from our steers, by the time we brought the horses on) from DPI.
This is very exciting! Take your time and be very, very objective when looking at horseflesh - with your level of experience (from what you've written, without further elaboration) it sounds like you can't afford to make any decisions from 'the heart' yet.
Equiculture will not lead you astray. The package of booklets she has is top notch - I have them all and they are our bible for the horses! Which reminds me, I have to give her feedback on them, as I was one of the first people to have the whole new set
We just drenched our horses, only one has rugs on (and he's not mine - he was looking too skinny and a bit poorly, so asked the owner to come and rug him to see if it makes a diff, if not he'll go back to her previous arrangement till she gets her own property), we just moved them to a strip for grazing before we turn them out into a bigger paddock with more grass for winter (we're on 160 acres, so have a few more options to play with, but never as much as I'd like!) and I may be looking at getting in hay for them. They're unshod and I plan to keep them that way. I had a horse chiro out yesterday for the buckskin for some soreness her loose patellar ligament has caused and that set me back $95, but probably cheaper than a vet call out. The horses won't always need a vet, there may be some other service you can use before using the vet. Someone at Pony Club or the riding school is always outgrowing tack and clothing, so keep your eyes peeled for that second hand gear. And rugs, if you must get them, are far cheaper online - the synthetics are all made in China anyway (and most canvas, too, except Skye Park rugs, from the big commercial brands; you'll always get local makers which cost more and come with great service), so go online if you can.