I'm wondering when you moved bub to the cot?

DD is in a basinette, Mother's Choice Coco (google it, its different from other basinettes). And I'm wondering if she's old enough to have some daytime sleeps in the cot.

She's 4 months old, but still only 9lb 8oz. my tiny tiny bubba
And her basinette matress is tilted because of her reflux...
And its got her special cushions in it to help her head mould into a normal shape, being in NICU so long her head was really long and flat on the sides.
Plus another rolled up towel under her bum to make her feel safe.

So, what do you think??
Another few months in the basinette?
Or a daytime sleep in the cot?