reading over your routine the first thing I think of is that your LO is overtired and thats why she only has short naps.
When you start your day at 8am, I'd suggest that you start with a feed. Granted she just ate at 6 but if you can start her in the habbit of starting her day at 8 then she'll strat to drop the 6am feed.
At 8am rather then putting on the DVD try doing quiet time activities with her, laying her under a play mat, reading, or even singing. To much stimulation is gotten from TV at such a young age. If you can get her to learn to play on her own then you can still get work done but have a calmer less overstimulated baby.
At 9am put her back down for her first nap. This will give her a chance to get a good start to her day, use pat/shush or PU/PD to help her extend that nap to be 1.5 hours rather then 20minutes. when she wakes do a little more quiet activity.
I would also suggest you try cutting out the solids for a couple more weeks till her new routine is settled. At 11:30-12 feed her and then do more activity more mat time or do some sitting activities, or excersauser if you have one. 12:30-1 put her back down for her second nap, do pat/shush or PU/PD to once again extend that nap to 1.5 hours again when she wakes more quiet activity, at 3:30-4 feed her again, the a little more activity time, then a 5 put her down for a cat nap (about 45 minutes) at 6pm start her bedtime routine, I recomend a bath, then storied/song and then her final feed and in bed by 7. At 10:30-11 dream feed. the at night try PU/PD or Pat/shush before feeding to try and settle.
Eventually your LO will start to sleep better and be a lot less overtired. The better her daytime naps the better her night time sleep.
Keep in mind that this is a guideline, ajust it to fit your LO, if one day your LO doesn't want to nap, but instead just lays in her cot quietly thats ok, its still restfull for your LO, she wont always have 1.5 hour naps, but you want to try and encourage her to start having them.
If you have any questions feel free to ask.