BEATRICE: Good Lord, for alliance! Thus goes every one to the
world but I, and I am sunburnt. I may sit in a corner
and cry ‘Heigh-ho for a husband!’
DON PEDRO: Lady Beatrice, I will get you one.
BEATRICE: I would rather have one of your father's getting.(285)
Hath your Grace ne'er a brother like you? Your father got
excellent husbands, if a maid could come by them.
DON PEDRO: Will you have me, lady?
BEATRICE: No, my lord, unless I might have another for working
days: your Grace is too costly to wear every day. But I(290)
beseech your Grace pardon me. I was born to speak all
mirth and no matter.
DON PEDRO: Your silence most offends me, and to be merry
best becomes you, for out o' question you were born in a
merry hour.(295) (II.i.)
This conversation takes place between Don Pedro and Beatrice in the beginning of the second act. Everyone is making merry, and the banter (and some rather racy puns) is going about among the men and women. Hero and Claudio are just betrothed, and the sight of the happy couple has made Don Pedro think of his own marriage.
It's important to understand that Don Pedro and all his men are recently back from a war. They are done with fighting, and now is time to relax, make merry, and, especially, to marry and make sure that they carry on their family lines. This is important for all the noblemen in Don Pedro's company, but for him, the Prince of Aragon and the highest ranking nobleman of the company, it was particularly important.
For noblemen several things were very important in a bride, but two were uppermost (as we have seen with the trouble between Claudio and Hero): that the bride is a virgin, and that the bride is from a noble family (preferably rich). Beatrice fulfills one of these requirements (she has made a funny joke about hell being "no place for your maids"), but she also makes the joke that she is too far below Don Pedro in rank, and that she would need a lower-ranking husband for "working days" -- implying that Don Pedro is too fine a husband for her, and is fit only for Sundays for her! In this she parries his heartfelt proposal with a gentle joke, which Don Pedro takes very well. He seems quite in love with her, and admires, especially, her verbal brilliance and tendency to jokes and puns.
So what kind of woman would Don Pedro need? He needs a wife, in order to carry on his line and ensure a peaceful succession in Aragon. He is an authoritative man, with what appears to be good judgment (most of the time). A woman like Beatrice might be his preference, for her intelligence and sense of fun, but primarily a wife of royalty like Don Pedro needed an aristocratic (if not royal) pedigree, and the ability to be diplomatic and manage a large household. By no stretch of the imagination could Beatrice be considered diplomatic.
It appears that Don Pedro is not yet ready for this serious undertaking, for he has spent his time with women who are not right for him, or actually refuse him. Perhaps he is preparing himself for marriage, which, as a high-ranking person would be more about his dynastic concerns than his personal preference. There is not much directly said about this, but it appears that Don Pedro is wrestling with this fact, and preparing himself to do his duty. And after the Hero fiasco, there seems little doubt that Don John will be in the Prince's disfavor for some time. After his wedding Benedick has threatened "brave punishments" (V.iv.129) for Don John, to which Don Pedro tacitly agrees (we assume). Who knows how severe these will be, since Pedro and John are related, but a wedding invitation will probably not be among them.