As Copernicus said, on Maemo you can usually use USB Networking ("SDK Mode") + ssh:

"adb shell" becomes just "ssh"
"adb push/pull" becomes "scp"
"adb sync" is roughly rsync-over-ssh (rsync for Maemo)
"adb logcat" would be something like tail -f'ing (that's "using 'tail -f' on") files in /var/log/
"adb forward" becomes "ssh -L..." or "ssh -R..."
"adb install/uninstall" becomes a small shell function that does scp + dpkg -i as ssh via root

Some of the lower-level features like serial number and other things can be obtained via flasher when the Maemo device is in flashing mode (flasher is roughly comparable to fastboot in terms of what it's used for).

For deploying to the device in Android SDK style, there's also MAD Developer (on Harmattan: SDK Connectivity Tool) - and you would use these tools with Qt Creator. MAD Developer and SDK Connectivity Tool can also be used to set up USB Networking (on Harmattan: selecting "SDK Mode" when USB is connected is enough).

Nitdroid also has adb support over USB networking, maybe you could re-use binaries from there if you want to have a real adb server on the device.