I'm a reading specialist. At 4, she doesn't need to know how to read. Kids learn how to read in kindergarten. For some it is 1st grade. Neither of my kids could read when they started kindergarten, but I had a lot of people assume that because I'm a reading teacher my kids would learn how to read early. Nope, they just were not ready. And I didn't really do anything special to teach them how to read. Now, they both are excellent readers.
Right now, focus on her recognizing her name and knowing the letters in her name. If she can write her name that is great, but at 4 it's ok if it is far from perfect. If she still mixes up b and d or m and n that's ok. I see kids as old as 3rd grade who still mix up some letters.
Sing the ABCs every day. Do alphabet puzzles. Read ABC books. Point out the big M on the McDonald's sign or the big K on the Kmart sign. Stop and look at signs that are low enough where she can trace the letters with her finger while you say them. Read to her. A LOT!!
Don't let anyone make you feel bad because their kid was reading at 3. It rarely happens. Don't waste your money on workbooks, iPad apps, Teach Your Baby to Read videos, or anything else. Get a library card. Cut pictures out of magazines to make your own ABC books. Make it fun.
As hard as it is not to, don't compare your kids. My daughter was closer to reading at the start of kindergarten than my son was. By mid-kindergarten, my son was reading better than my daughter was at the same point.
Go ahead with the speech screening. Most school districts also have early childhood screenings for 3-4 year olds that are designed to catch delays. Ask the speech evaluator or pediatrician or call your school district. Good luck!