I apologize for not remembering anything about her reading progress in the past...so if I'm repeating myself or making you repeat yourself, sorry!
The foundation of effective reading for any learner of an alphabetic language (such as English) is phonological awareness. I am not familiar with the approach of Reading Eggs, and could not see this information on their website, but I would be concerned that PA skills are not being instructed. Something like 2/3 of kids figure them out without instruction, but another 1/3 (not necessarily LD kiddos, just not natural phonics kids) really need explicit instruction in phonological awareness from the ground up. Otherwise, they spend their time doing what your daughter appears to be doing, which is sounding out initial consonants, and then guessing at the rest based on context. This is so common that there is actually a term for it in the reading research literature ("the psycholinguistic guessing game"). Unfortunately, not all reading programs are based on the past 30 years of research, and continue to use more-or-less whole language approaches (aka, the PGG referenced above). These programs don't get weeded out by the market, because they work on the 2/3 of kids for whom repeated exposure to any literacy instruction at all (or none, but repeated exposure to reading in general) will result in reading mastery.
At age 4.5, she should have some PA skills. Here's one chart with some examples of the developmental sequence of PA:
http://www.readingrockets.org/article/development-phonological-skillsTry surveying some of her PA skills (sounds like it might take you a few sessions!), and see if there are gaps, or stuck places. You may also discover that the process of assessing her helps her to learn these skills, as they may never have been presented to her before.
