Blueskies, I know you'll get a lot of messages saying "you have to allow X years (where X is some large-ish) gap". But I remember sitting in on a conversation my mum had with one of my friends back when he and I were in our twenties. His mum had died a year earlier, his dad had got engaged to one of their mutual friends, and he was understandably upset about it.
My mum (born 1929) who had seen her mum "replaced" by a (rather unpleasant) woman, but who had also seen lots of other friends re-marry happily after being widowed (so she'd seen a wide variation) explained that back in her generation when premature death was more common, people tended to remarry quite soon afterwards, and it was (in her experience) usually a testament to how happy they'd been in their first marriage. In mine and my friend's generation, in contrast, the model we had for seeing relationships end was unhappy breakups rather than bereavement - and that did take a long time to get over, because you hadn't lost a loved partner, you'd lost confidence in the possibility of happy relationships and confidence in your own judgement when it came to choosing partners (my mum knew what she was talking about on that one too - her first marriage had ended in divorce, quite unusually for the time). Where you'd lost a partner to death, you still believed in happy loving relationships because you'd been in one. So in her experience, bereaved people "moved on" more quickly than divorced people - except that in an important sense they didn't move on. Bereavement was a very odd situation where people could love two people at once and that was okay - they could love and treasure the memory of their late spouse and love their new partner. And that was okay.
It's a conversation that's always stuck in my mind, because I've seen it happen a couple of times among friends my age and younger (interestingly, one man, one woman - both of whom lost partners to accidents - they both went on to marry mutual friends of theirs and their late partners relatively quickly).
So, in short, my mum's take was that it isn't disrespectful to your late partner, it can be testament to just how strong and loving your first marriage was. (But at the same time, that those around you may not understand this).
Of course it doesn't always work this way - my mum died about 10 years ago now, and it took my dad at least 7 or 8 years before he felt ready to see anyone else (and even after 7 or 8 years it did feel very weird for me - but as a child feeling weird and acknowledging that it's none of your business and your job is to do your best to feel happy for them is actually part and parcel of being a grown-up; I can see it's harder for teenagers or younger children, though).