I COMPLETELY concur about landmark notes, and intervallic reading, and recommend that you AVOID the e-g-b-d-f mnemonics. ESPECIALLY since your daughter is just a beginner.
The lines and spaces mnemonics can be problematic because, for one thing, it's easy to get confused and forget which is for treble and which is for bass. This means you haven't actually learned to READ the notes, you're basically counting on your fingers without actually understanding how to add, if you see the analogy.
It creates dependence on the mnemonic rather than an understanding of what the staff lines truly represent (ie, the relationship between pitches). I had transfer students who had been taking lessons for YEARS, who when asked to name a note, STILL would start mumbling "every... good... boy..."
Because they're mnemonics, it shows nothing about the relationship between the notes. I've actually known kids who learned e-g-b-d-f and f-a-c-e but never realized that the note above 'e' is 'f'.
Interesting fact: the best sight-readers are not NAMING every single note as they go. They follow the shapes -- the distance between notes, the patterns and rise and fall. Naming some notes, sure, but not every single one.
Again, I've seen kids look at a passage of 5 notes rising by step, who would stop and say "e-g-b... the first one is b... f-a-c... the second one is c..." having to name each note before they could find it and play it.
Anyway... a 7yo who has been taking lessons for a month and a half should not be working on memorizing all the note-names just yet IMO. They'd either still be in pre-reading materials or focusing on a couple landmark notes. They have to learn the note-names on the piano itself before the note-names on the staff will have any meaning to them.
I am speaking as a professional musician and registered music teacher, I have a master's degree in piano performance, and have been teaching for 15 years. There are MANY people out there who call themselves piano teachers but don't actually have any training or experience in how children learn to read and play music, they just pass on however they think they learned it themselves.
Learning to read music is a topic I've actually studied quite a bit. When I have had students who were with me from the beginning (as opposed to transfer students), I very deliberately AVOIDED e-g-b-d-f, and told them not to use it (and why) if they were told about it from other sources (often well-meaning parents...).
They all ended up being excellent readers, much better able to read independently and fluently.
Anyway, I don't know if I actually answered your question clearly, I kind of just went off on a spiel heh... What I would advise, truly, is that unless your teacher has specifically asked you to work on note-names, then DON'T. Your teacher may have a plan and specific method in mind already, and your well-intended coaching might end up interfering. Or, even if she was planning to use that method, it's too much too soon. She might be able to learn the 'trick' but that doesn't mean she really understands reading music.
If the teacher DID tell you to work on note-names, but didn't give any real advice on how, then 1) I can give some more concrete suggestions and 2) look for a different teacher! heh...
May I ask what method book your daughter is using?
Edited to add: I should say that the mnemonics DO have uses. Once someone is able to read fluently via landmarks and intervals, but perhaps is slow in calculating what a particular note-name is (not really important for playing, but absolutely essential for theory), then the mnemonics can be used as a quick 'cheat' for speed. But this is only AFTER understanding how to read the notes the "real" way. I think this should be the case for ALL uses of mnemonics and memory tricks. You don't memorize the times tables before you understand what multiplication even means.
Most of my students never needed the mnemonics anyway, once they reached the point of fluency they had just learned all the note names naturally along they way. But it would have a purpose in the situation of a student who didn't develop that on their own. But not as the INITIAL teaching tool. That's the MAIN point I must make. Mnemonics are an AID to memory AFTER a subject has been learned, and should NOT be the teaching tool itself!