A.,
I did not start 'quiet time', per se, with my son until he was three. This was based on my longtime experience as a nanny and toddler group/preschool teacher. For most toddlers, 30 minutes of independent play is shooting for the moon. Considering a child's attention span is usually one minute per age, try for five or ten or even fifteen minute intervals. From your post, I have to think your child is not ready for those longer playtimes alone yet.
Before three, what I did was to basically be 'unavailable' and busy myself. Sometimes this meant keeping myself standing up and taking a five minute break on the laptop at the counter (instead of sitting down). I worked in the garden, did dishes, folded clothes, etc. What worked very well was alternating between my housework and short playtimes, often to get my son started on something he could then explore on his own. Remember, toddlers do well with very open-ended activities; the other piece of this is that little toddler girls are often very social and want to play 'pretend' *with* us, so that is an added challenge.
Sensory activities, though, are wonderful for more independent play. I bought a big washtub for this and fill the first three inches with any of the following:
Rice
Dried beans
Barley
water
Bubbles and water
Noodles (macaroni-- you can color the mac or rice together with food coloring--just a few drops in a bowl, stir it round)
Place any of those items in a bin with some scoops, big spoons, funnels (you can make them for cheap-- just cut a plastic water bottle in half and cover the raw edge with masking tape). Fun, tho she should not be completely unsupervised, as usual with toddlers. Put a quilt or blanket on the floor beneath the bin for easy cleanup and a no-slip surface for water play.
FWIW-- kids get VERY into water play!
Some kids love to 'bury' little animal toys/small objects in a small box on a tray with small lentils or split peas.
Playdough is fun. Give her little pieces of paper (just recycled 1/2 and 1/4 sheets is fine) and a few crayons, some envelopes.... let her find her fun. A block set big enough to be successful with is great, and you can do the same with your recycled cereal/food boxes. Instead of flattening, collect a bag full, tape them shut and let her use them as blocks.
Tape a big piece of paper to the table and give her a few crayons. Or garage sale stickers. They are cheap and very good entertainment, plus help develop that all-important pincer grip.
Lastly, when you need to do something, be firm. "I'll hold you/play with you in just two minutes. I need to finish what I'm doing." At this point, I had to ignore the screaming when this happened. I want to encourage you to remember that this only works if her other needs (food, clean diaper/potty, not tired) are met... and remember that attention is an actual need as well.
The busy bags are a good idea and yes, make sure you help her get started.
Good luck!