Advice on whether to get a tutor.

Honestly I think you’re doing a lot and it’s OK that she’s taking her time. If you’re concerned you could always talk to her school and see what they recommend but you’re doing a lot more than I do with my 3.5 year old and she’s picked it up because she enjoys it and wants to do it (she’s lacking enthusiasm in many other areas, they all have their strengths). I’d chat to school, take the pressure off a bit, try to make it less structured and more fun like hey how many bits of toast are left?! Also if you use screen time at all I do recommend number blocks. My daughter LOVES them and it’s not all about the tv, she’s got the yoto card for songs and some toys. With letters we have physical items, magnets that she can carry round and assign to her toys for example. She loves getting me the M for Mama! I think there’s importance in supporting learning but I also think sometimes it’s too much and I don’t think that this is particularly concerning for a 4 year old.

I think you're doing a good job. Making learning something fun you do together will be really beneficial.
My son muddles up p/d/b and l/i too and he is learning to read but he's not confident. They are just 4 years old and I think it can be easy to worry about their progress.
Last week we had parents evening and his teacher said she was happy with his progress (and imo he isn't really "advanced" or ahead in anything, he's just doing the best he can at 4).
I second Rachel's comment about the Numberblocks! We also have the yoto cards but the same songs are on Spotify (if you use it) and we listen to those in the car.
Speak to your daughters teacher and see if they have a parents evening planned or simply ask if they have any concerns.