"Getting married then having the reception months later sounds very bizarre!"
Lots of people do it OP, for various reasons, but it was just a suggestion as you seemed to want to appease your sister in some way and it was one possible solution to doing that and I hadn't seen it suggested already on the thread.
I don't actually believe in all this thunder-stealing nonsense. Hundreds of people will get married on the same day as you, as your sister, as everybody else who ever gets married anywhere.
If next year suits you and your DP then that's when you should do it. Before her or after her doesn't really matter.
I mean, either you jump in first and 'steal her thunder' 
or you wait a few weeks after her wedding and 'steal' her place as the family newly-wed.
You've had lots of suggestions here, and you seem keen for an easter wedding rather than an autumn or winter one, as this is before the time you hope to start TTC.
If that's really what you want, you are going to have to do two things. Firstly you need to decide what the consequences of your decision might be and if you can live with them, and then secondly, talk to your sister, because that's the only way you might avoid causing her hurt or bad feeling, however unreasonable she may or may not be to feel it.
Has she sent out her invitations yet? And has she had all the acceptances returned?
If so, work on that basis, tell her that you will make it clear to your mutual guests that you know she invited them first and that they have made a commitment to attend her wedding, and on that basis you will understand absolutely if they cannot then attend your wedding because of financial costs or getting two sets of leave from work etc and you don't want to cause anybody to choose between either wedding.
Reassure her that you are prepared for the fact that this means some people might not come to your wedding but that you are absolutely not trying to 'steal' guests from hers.
Tell her your reasons, your DB leaving, your wanting to TTC, your need to work this around your DP's child access etc.
Make sure she knows that your wedding is about you, not her, and stress how different the weddings will be.
If you can talk to her reasonably and find out exactly what's worrying her, and reassure her that you are taking her concerns seriously and trying to avoid everything she is worried about, then that should be good enough for her.
You can work with reasonable concerns, such as worrying about guests or finances, but you can't pander to unreasonable ones, such as thunder being stolen from her.