my advice would be biolage hair serum rub it in your hands and start at the end of her hair after it is wet and work it up to the roots,this will help control the frizz,follow w/ tigi curls rocks it's awesome for keeping the curls together and it doesn't make hair hard,or greasy.never blow dry curling hair without a diffuser it will get frizzier, my 11 month old, I sit one my lap with the hair dryer w/ diffuser and just let it do it's thing,with curly hair if you brush it after it dries more frizz.
getting a 15 month old to sit still is impossible, and in order to smooth the hair you need heat which is hardly an option at such a small age.depending on how coarse her hair is pomade is great for keeping the frizzes under control to get her hair up,dove makes one I like, I would try styling it up wet after working the pomade through ends to root.
I suggest just using some light hair products for now. as for trimming it in the future, take her to a hairdresser that knows bi racial hair,it cuts much shorter then caucasian hair and you need sharp scissors to avoid more frizz. When she is older you could consider getting braids or twisties done around her hair line if it really bothers you but it does require the hair to be pulled taunt which will be rather uncomfortable for her.
It hard to understand that there is so much of a difference with white and black hair care they invests losts of time, and money for beautiful hair it's more then just hair for them, very few have the luxury of just washing it and letting it go.
Hope this helps have a great day.