I know it's completely reasonable and I won't say no but it just feels a bit 'off' they had their offer accepted and 3 days later were asking to measure up. We have another 2 weeks to exchange and 4 after that for completion.
If you've not got your own personal things everywhere because you're packing up then they might be able to envisage it even more as their own house, iyswim, rather than yours. Their's is possibly half packed too. I think it's good of you to let them measure up. When we moved we bought a brand new house and we weren't allowed in to measure for anything until we'd moved in!
They will be very pleased to see lots of boxes being packed. It suggests that you ate getting on with things and won't drag your heels. The measuring up is a good thing. It means they are making plans and are less likely to drag their heels. This is a win-win situation.
Unless you go to Ikea you need to order stuff in advance otherwise you are living out of he box for six weeks before the furniture arrives. They might me moving from a furnished rental and need to buy everything.