Enjoy your sweet baby girl while she still relies so heavily on you for comfort, food, and sleep. Enjoy every moment of holding her while nursing/bottle/sippy feeding! Those days disappear so incredibly quickly and you wonder how your little girl suddenly seems so big and grown up... :)
So my advice? Slow down. Your daughter is still a little baby - she's only 9 months old, right? Very, very few babies that age can or (even should be, on a regular basis) holding her own bottle or sippy cup. Also "bottle propping" is never recommended (where your baby can't hold it, but something other than a human hand is used to prop the bottle up into her mouth).
Please don't feel rushed into your daughter holding her own sippy or bottle. You're her mom - it's the parents' job (dad's too!) to nurture her while feeding, holding the bottle, cuddling her, taking the time to just BE with her. That's where they learn trust the most - the more times you repeat it with them (being there for them, helping them when they truly, developmentally need help with it!) in these first years, the better!
Also, to the speech therapist who lumped bottle & sippy cup feeding in with breast feeding when it comes to complex sucking actions - getting milk from the breast and drinking from a cup BOTH require more complex muscle coordination than sippy or bottle feeding. Preemies are often encouraged to cup-feed until they're strong enough to breast feed because the muscles developed are so similar. So if any breastfeeding moms are reading this, don't worry about your child's speech!!! In fact, rest assured that there is only evidence that speech is *positively* affected by breast feeding, not negatively, regardless of how long your baby or toddler nurses:
Breastfeeding and Speech Development
http://www.kellymom.com/bf/normal/speech-development.html