Is it unusual not to be counting/singing nursery rhymes by 2YO?

[Jannt86]

My just turned 2YO has always been hard work with her talking. Didn't babble until almost 12MO, always seemed to struggle a bit to produce sounds. Now at just turned 2YO she does say quite a few 3 word phrases although quite unclearly (probably only someone close to her would understand most of it) She's also nailing potty training atm and really took to it well. She also does multi-piece jigsaws with ease and recognises some (I think l) some quite clever spacial things eg when something is 'inside out'. She is also lovely with all kinds of imaginitive play. However, she doesn't seem to have any ability or desire to rote learn nursery rhymes or counting or anything. I sing a lot with her and sometimes she signs the actions and enjoys if she can be bothered but a lot of the time she just gets annoyed and tells me to stop. She can recognise when there's 2 of something and says it ie; '2 dogs' and sometimes mimicks counting and even recognises most of her numbers but has never made any effort to count her numbers out loud even 1,2,3. She will also finish sentences of most of her books if it's a word she knows and I prompt her. She even astounds me with this finishing the sentences when it's a book we haven't read for ages. She's never been one for watching me gooey eyed and copying my facial expressions or anything and I'd say even making eye contact with her can be hard work. TBH she's only in the last few weeks started parroting what I say. However I just don't know how 'typical' all this is. Will she eventually just do it? Is it a behavioural thing or an ability thing? I'm just confused at all the other clever stuff she can do but she can't do this? I've always felt that there's a bit of a niggle and a lag with her expressive language compared to everything else but just never quite been able to put my finger on it and every time I think we're doing find I start to whittle again I'm always telling people on here not to compare and I try not to but when I see the majority of kids her age and even younger joining in with nursery rhymes etc it does make me worry.

It is probably not that unusual, at this age they will have their own likes and dislikes - how is her non verbal communication? like pointing to share interests (plane in the sky), social referencing, praise seeking, etc.

She's been pointing whole handed since 9MO turning into a single finger point at around 14MO I think and was clapping and waving etc from about 9MO too and could self-initiate peepo at 7MO. She's stubborn and defient at times but not excessively so I wouldn't say. I'd say she's pretty praise driven yeh. I'm sure that's why she's been so easy to potty train. She has a good sense of humour and regularly does things to get a laugh too. Like you say it is probably just that she simply doesn't want to do it or is waiting til she can be really perfect with it. I just find it quite perplexing though that her expressive language although perhaps not majorly behind has always lagged behind everything else. I guess it'll come at some point though