Ooo how exciting. I am very impressed that your daughter is trotting already at 2, very advanced!
Word of mouth is how good ponies are found in my area, the best are never advertised but are swapped around families acquainted with one another, mainly through pony club contacts. Obviously your daughter is a bit little to join yet but maybe worth contacting your local PC branch to see if anyone has a suitable pony that is outgrown and looking for a new home?
In terms of what to look for, for me I would want a pony proven to do the job, i.e. that has already been regularly ridden by very little ones, in a family situation, not a riding school or at a dealers or similar. On a viewing I would want to see it handled as much as possible by their child rider (obviously not as young as your DD!) through all normal activities, bringing in, grooming, tacking up, getting on and off, ridden (on a lead) in a school, on the road and in an open space. Ideally I would like to see it at a show or PC rally or other group situation too (and this gives you a chance to verify that the pony has been around on the local scene and is not a known nightmare too!).
I wouldn't be too hung up on breed, looks or sex (although for something small enough you'd likely be looking at a shetland or welsh A I guess?). I also wouldn't mind too much if it isn't very good off the lead rein as your DD is presumably a way away from needing a first ridden yet.
Age is important to me in kids ponies, I won't look at anything younger than 8. That's not to say that younger ponies can't be brilliant too, some of my friends have bought 5 or 6 year olds for their kids, I just prefer something more proven as they can change so much through their 'teenager' years and I don't like to take the risk. Tiny lead rein ponies can go on well into their 20s and your DD is not exactly going to be doing strenous work with him/her so I wouldn't rule out a golden oldie who will appreciate a quiet life and lots of fuss!
Good luck, keep us updated!