Personally, I would not even think about getting on a horse until they're 3 - a horse's joints are not finished forming until they are fully grown, and working them too hard early in their lives can mess up how their legs develop. You wont see problems for years down the road, but if you plan on having this horse for a while I would wait.
Plus, now you have plenty of time to do lots and lots of groundwork! This is the most important piece of training a horse and is what will build your horses trust in you.
Again, too much can be bad for her baby joints, so take it slow. Three 15 minute training sessions per day is worlds more valuable than one 45 minute session, especially for a young horse. Just like kids, they have a short attention span and get frustrated easily - so keep that in mind.
I am a fan of free lunging (or round-penning) so I would look into that, also this is your chance to desensitize your new girl to all sorts of things! Get her to wear a tarp aon her head, lead her along the road (safely) so she is used to cars going by, put that saddle on every day, have her work with a bit in her mouth (no reins)
I'm not saying you can't get on her and even walk around, but keep it at that for now and don't do it very often. When you do - go crazy with praise. Make her feel like the most amazing horse in the world while you're sitting on her. Save a special treat for that occasion even? This way, she will forever associate you being on her back with wicked warm fuzzies. Remember to keep this going later in her life.
Have fun with her - what a cutie!