Hi,
Do not worry! I put a posting on here a couple of weeks ago - I have a 2 year old bitch and introduced a new puppy. After 6 weeks my 2 year old still growled and sulked with the puppy. The responses I got from COL were that this is normal and could take 6 months for them to settle! - and I have to say, that as time has gone on their relationship has got better.
Has Milly been the only dog in your household for 4 years? If so, she is probably a bit miffed about the new comer - wondering who he is, why he is here and of course, why he is taking some attention! We always make sure that visitors to our puppy still said "hello" to Jessie (the two year old) first, so she did not feel too left out and get jealous.
Just leave them to it for now and just keep a watch. Milly will get curious about him in the end. She may start to boss him to let him know this is firstly her territory but as long as it is not vicious, this too is normal. After only a day and a half, I would say that Milly needs more time to adapt ....
Do let us know how their relationships develops!