'Have you set a date yet?' this question, along with 'How did you do it?' and, 'Let me see the ring?' is the great triumvirate of post proposal questions. Prepare yourself for it, people will show interest and you should be grateful rather than exasperated. Also, they are not hinting at an invitation, regardless if they say something like, 'great, I'll just pop that in the diary', they are joking, and if you respond with some indication that you are having a small wedding that won't accommodate for them, you just make things awkward.
But a wedding does need a date, and you will be amazed at how fast and far in advance these dates get booked up. Me, I proposed in February and knew that, as peonies were Mrs. Editor's favourite flower, that there was a May/June window that the date needed to be set. Three of four months is not enough time to plan the wedding, so just under a year and a half was ideal for setting the date.
A few things to think about: work will probably be thrilled for you that you are getting married, but don't think they will be ok with you leaving them high and dry as you take off for wedding preparations, and then a 2 week holiday where switching your phone off will be an imperative. Also remember that setting a date will need the sign off from more than just you and your bride (or fellow groom of course). A quick whatsapp to your ushers, in-laws and most importantly, friends who are already engaged, or who you think are about to make the leap. This is very important as a wedding should have the people you love there, and if you are just slapdash and don't take people into account, you will regret it, unless you have no soul, or friends. Also, if like us, your wedding is to be abroad and you set a date with less than a years notice for your guests, you are being incredibly inconsiderate, so don't do that.
Once you set a date, decide and get 'Save the Dates' out as fast as possible for people to, well, save. Collate email addresses as fast as you can, if you are using paperless post like so many young folk these days, then put together something straightforward and please, nothing too whimsical or straight out of Disney, there is a thin line between romantic and schmaltz, don't cross it. It should instruct people to give over information such as postal addresses (while save the dates can be over email, wedding invitations certainly should not be). After that, Congratulations, you have yourself a wedding day.
PS: To make it simpler for you, if peonies are her favourite flower, your wedding will be in May/June.