Before you can think about cloning an organism, you need its complete set of genes, or genome. You're extremely unlikely to get that from whatever DNA you've extracted from the mosquito, so you're going to have to improvise.
If we were to clone a mammoth or neanderthal, we could use an elephant or human's genome to work out where each scrap of DNA goes and start reconstructing the whole genome.
In the film of Jurassic Park, scientists fill in the gaps with frog DNA (the book mentions using the DNA of other animals, too).
But actually the best candidate for filling in dinosaur DNA would be birds, says Brian Switek at Mental Floss. They are the only living things left over from the time dinosaurs roamed Earth. Even so, their use in helping us figure our dinosaur genomes would be "quite limited".
From this patchwork genome you then need to construct some chromosomes. Sadly, we don't know how to do for dinosaurs.