11 month old doesn't feed herself! HELP!

Rachel • Aussie :) I'm 31, he's 35, our son will be 4 in Feb, daughter born Oct 2016

TL:DR - my daughter doesn't feed herself yet, should I be worried/take her to get checked out? And by who, paediatrician? Occupational therapist?

Quick back story - mum of 2, son was holding rusk sticks and sweet potato chips etc at 6 months old & putting it in his mouth to eat them (below), daughter who's 11 months doesn't.

Daughter will be 1 at the end of Oct & doesnt. At all. On the plus side she also doesnt put anything else in her mouth like toys, bits of fluff on the floor, money, dirt (oh man my little sis was so bad with those things), or her dummy.

The only way she'll eat is if we put it in her mouth for her, doesn't matter if we use fork, spoon, our own fingers, chopsticks etc she'll eat it.

Both bubs started solids (rice cereal) at around 4 months, and both have been amazing eaters (son is 4.5 & loves sushi (raw salmon & rice, edamame (soy beans) calamari rings & tuna & avocado rolls), Thai (Satay chicken skewers, spring rolls etc), Indian (goat curry, butter chicken with rice & naan bread), he loves fish, vegetables, fruit etc daughter has tried most things we eat (same as son above, last night we had sushi & she had a tuna & avocado roll, some teriyaki salmon & adagashi tofu, she's had massaman curry with coconut rice, butter chicken sauce with naan bread etc), both got teeth late (son cut his first at 11 months, daughter is 11 months and no teeth yet), both hit milestones around the same time, rolling, sitting, crawling etc.

But she just refuses to feed herself. I've tried giving her little bits of things to hold - sandwiches, grated cheese, rusk sticks, fries, scrambled egg, tofu, pasta, mini ravioli, fruit bars (baked bars with squishy fruit in the middle), but she just squishes them in her fingers then throws it. I've tried putting it in her hand then taking her hand to her mouth (she drops the food and shakes her arm to get away), I've tried giving her a spoon too (she just looks at it), I've tried showing her how I pick up food off her tray & put it in my mouth. I've tried putting it in her hand and opening my mouth so she'll feed me (she'll put her dummy in my mouth but not food). She's just started putting her dummy in her own mouth & I cheer & clap & she smiles, and she occasionally chews on toys.

Should I get her checked out? I'm worried that she seems completely against it. If I do, who do I go see? A paediatrician? Occupational therapist? Her fine motor skills are excellent, at a young age she was picking up minuscule bits of fluff and rice etc.

Tofu!

First try of yum Cha!