You're not doing anything wrong. You're noticing the very
common—yet agonizing—catnapping pattern of younger babies. My sense is that this short napping
phenomenon is partly because we put babies on their backs to sleep (which we do
for good reason, as the back-to-sleep campaign has cut the rate of SIDS
significantly with this recommendation). But many babies are more easily roused
on their backs.
Hang in there. When your baby is unswaddled and can roll,
these catnaps will grow. Make sure you're doing a lot of tummy time—once she
can roll and move, she can choose her own sleeping position and sleep longer.
She's also much more likely to take a longer nap if you put
her down in her crib awake and allow her to do the falling-to-sleep part
herself. (Try it once a day, you might be surprised that she can do it.) If she can self-soothe at the beginning of a nap, she'll know just what to do when she
startles, comes into a light stage of sleep or is woken by a noise. She'll be
able to put herself back to sleep (rather than being surprised and confused
about where she is, since she went into her crib unknowingly).
Also make sure to put her down frequently enough—after 90
minutes of awake time if she under about 5 months of age (yes, 90 minutes after waking, put her back down). If you miss the
window, she may be more restless and more likely to take a short nap.