I'm on my phone so I can't see how old dd is?
I have had similar problems with all my three and honestly putting my now 5 month old in the hug a bub to get sleep was the only thing that worked...from around 6 weeks till about 14weeks it was a battle.
He now self settles and sleeps mostly in his cot ( I do pop him into bed with me if he wakes before 6am and I get another hour or so sleep)
So I honestly don't think she will come to expect it. They as bubs need to be close to you and them gradually want their space as they grow just like we need it to!
Get sleep anyway and anyhow you can because its hard enough being a mum let alone a sleep deprived one too!!