I used to be a pre-k teacher for Toddlers (approx 14-24 months old) and also an assistant teacher for the 2's & 3's classroom.
At 2.5 years old, your daughter should be doing things like pretend play (playing dress up, playing kitchen, pretending to talk on the phone like mommy, etc), sort and match colors and shapes, should understand the concept of big and small (as well we under/over, top/bottom, etc), use negation in speech (telling you she doesnt want or like something, for example, by saying "I no want" or "I no like", etc). She should be able to stand on one foot without assistance, jump up and down, stack blocks (many of them, like 6-10), and understand the concept of "one" - like bringing you one block instead of all of them.
Activities you can do are practically endless. Since she isn't in pre-k, you can act as her teacher. In pre-k, the day is divided into parts - free play, structured activities, meals, and nap. Free play time is when the kids can go play at the different centers in the room - dress-up, blocks, fine motor (like threading yarn with a plastic needle through holes), etc.
Try picking a theme each week - like "Farm", "Water", "Zoo", "Colors", "Shapes" etc. You can get ideas from books at teacher supply stores. Then for each day of that week, do a few activities with her. For farm for example, you could get together with other kids (if possible) and play farmer in the dell (or just sing it) and that's a music activity. Read a book that about farm animals to her (reading/language) and encourage her to repeat their names and what sounds they make while pointing to the pictures. Print out (from online or out of an activity book) pictures of animals for her to color - with crayons, finger paint, tissue paper (and glue), etc (art project). While working on the art project, tie it in with the language. If she's coloring a pig, ask her "what does a pig say", "what color is a pig" etc. Do a different animal (or a couple different animals) everyday, and hang her artwork up for her to see - in her room, on the fridge, etc.
Fingerplays are great for this age and you can make them using felt and velcro. You can then tell stories (using music and songs and spoken word) for a variety of themes. Get a fingerboard story book from a teacher supply store and the possibilities are practically endless!
Just as with the "Farm" theme used as an example, you can start with simpler themes like "colors". Learn about one color on the morning and one in the afternoon or stretch the theme for two weeks. Let's today today's color is green. Put several green objects in the room you'll be in. It's helpful if you have the same items in multiple colors (like a green spoon, a yellow spoon, and a pink spoon, for example) and ask her to bring you the green one. If she chooses the right one, clap (and say YAY!) and make a big deal. If she chooses the wrong one, tell her, "no, that's (insert color). I'm looking for the GREEN one". Dress her in that color and you can help her make connections "GREEN like your SHIRT!". Paint or color with crayons that are different shade of green. Read Green Eggs & Ham and actually make it to eat if you're up for it (this worked better with 4 & 5 yr olds but the 2&3's still enjoyed the activity). Make Green Beans, Peas, etc to eat. If the color if the day is Red, then serve red foods, dress her in a red shirt, etc.
When I was a teacher, our schedule was predictable and the kids worked well with it. First thing we'd serve breakfast, and after that we'd let the kids have free play (supervised, of course) while we cleaned up breakfast dishes and got the materials ready for our structured activity - usually art. After art, one of us would read a story or do a flannelboard play (both language arts) while the other cleaned up the art mess. Then we'd let the kids have free time again - either inside with the blocks, etc, or outside. Then we'd usually have a sing-a-along while we got lunch on the table. After lunch, it was naptime. Once the kids got up and had a snack, we'd let them play outside (15-20 minutes) while the nextt activity was being readied. That could be a fingerboard play, book, music, another art project, we all play dress up (very fun during community helper week!) etc, followed by freeplay inside, one more song or story, and finishing off the day with outside time.
Sorry I know my response is a bit disorganized but just typing as they come to me (in between getting something done at work!). Pick up some books at a teacher supply store to get started with some ideas. From there, let our imagination take over and before you know it. your daughter will be equal or ahead of her peers that attend pre-k.