It is NOT reccommeded that a 15 month old sleep in a bed! At this age, they are still babies - she clings and cries when you put her down because she wants YOU, and not to sleep, not that she feels she is trapped in her bed. If you put a 15 month old in a toddler bed, you are asking for it - she will get up over and over all night long, and I guarentee you, she will not sleep at all because she has the option of getting up and down whenever she wants.
She is likely just going through a cling to mommy phase, or an "I dont want to sleep" phase. 15 months is a HUGE milestone month, one of the months that pediatricians and child psychologists consider the most important month of development. She could be wanting to stay up for a variet of reasons, but do not think that you can fix them by putting her in a toddler bed. In fact, you would be inviting stress and anxiety in both of your lives: it is very important that you keep her routine how it has been so that she has consistancy.
Here are a few ideas to make her more comfortable at bedtime:
-Consider putting her to bed later than you currently do, as it will be easier for her to want to go to sleep.
-Does she still take two naps a day? If so, consider taking one of them away so that she is tired at the end of day.
Often, children give up one of their daytime naps at this age. She may just not be tired enough at night, and puts up a fuss because she's not ready for bed yet.
Im a child psychologist, and have experienced this question MANY times in my practice. Feel free to email me for any more ideas!